KILLED
proof of input_jtSlOxgEDE.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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), 21 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (14) CpxRNTS
        (15) InliningProof [UPPER BOUND(ID), 0 ms]
        (16) CpxRNTS
        (17) SimplificationProof [BOTH BOUNDS(ID, ID), 57 ms]
        (18) CpxRNTS
        (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 3 ms]
        (20) CpxRNTS
        (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (22) CpxRNTS
        (23) IntTrsBoundProof [UPPER BOUND(ID), 146 ms]
        (24) CpxRNTS
        (25) IntTrsBoundProof [UPPER BOUND(ID), 8 ms]
        (26) CpxRNTS
        (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) IntTrsBoundProof [UPPER BOUND(ID), 194 ms]
        (30) CpxRNTS
        (31) IntTrsBoundProof [UPPER BOUND(ID), 33 ms]
        (32) CpxRNTS
        (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
        (35) IntTrsBoundProof [UPPER BOUND(ID), 103 ms]
        (36) CpxRNTS
        (37) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
        (38) CpxRNTS
        (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (40) CpxRNTS
        (41) IntTrsBoundProof [UPPER BOUND(ID), 131 ms]
        (42) CpxRNTS
        (43) IntTrsBoundProof [UPPER BOUND(ID), 55 ms]
        (44) CpxRNTS
        (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (46) CpxRNTS
        (47) IntTrsBoundProof [UPPER BOUND(ID), 313 ms]
        (48) CpxRNTS
        (49) IntTrsBoundProof [UPPER BOUND(ID), 127 ms]
        (50) CpxRNTS
        (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (52) CpxRNTS
        (53) IntTrsBoundProof [UPPER BOUND(ID), 342 ms]
        (54) CpxRNTS
        (55) IntTrsBoundProof [UPPER BOUND(ID), 95 ms]
        (56) CpxRNTS
        (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (58) CpxRNTS
        (59) IntTrsBoundProof [UPPER BOUND(ID), 79 ms]
        (60) CpxRNTS
        (61) IntTrsBoundProof [UPPER BOUND(ID), 72 ms]
        (62) CpxRNTS
        (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (64) CpxRNTS
        (65) IntTrsBoundProof [UPPER BOUND(ID), 106.5 s]
        (66) CpxRNTS
        (67) IntTrsBoundProof [UPPER BOUND(ID), 41.6 s]
        (68) CpxRNTS
    (69) CompletionProof [UPPER BOUND(ID), 35 ms]
    (70) CpxTypedWeightedCompleteTrs
        (71) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (72) CpxRNTS
(73) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(74) CdtProblem
    (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 4 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 84 ms]
    (88) CdtProblem
    (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 91 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 104 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
    (104) CdtProblem
    (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 128 ms]
    (110) CdtProblem
    (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 172 ms]
    (144) CdtProblem
    (145) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 250 ms]
    (146) CdtProblem
    (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
    (152) CdtProblem
    (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CdtProblem
    (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (160) CdtProblem
    (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 269 ms]
    (168) CdtProblem
    (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (170) CdtProblem
    (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (172) CdtProblem
    (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (174) CdtProblem
    (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (176) CdtProblem
    (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (178) CdtProblem
    (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (180) CdtProblem
    (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (182) CdtProblem
    (183) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (184) CdtProblem
    (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (186) CdtProblem
    (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (188) CdtProblem
    (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (190) CdtProblem
    (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (192) CdtProblem
    (193) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 422 ms]
    (194) CdtProblem
    (195) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 331 ms]
    (196) CdtProblem
    (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (198) CdtProblem
    (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (200) CdtProblem
    (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (202) CdtProblem
    (203) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (204) CdtProblem
    (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (206) CdtProblem
    (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (208) CdtProblem
    (209) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (210) CdtProblem
    (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (212) CdtProblem
    (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (214) CdtProblem
    (215) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (216) CdtProblem
    (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (218) CdtProblem
    (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (220) CdtProblem
    (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (222) CdtProblem
    (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (224) CdtProblem
    (225) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 550 ms]
    (226) CdtProblem
    (227) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 508 ms]
    (228) CdtProblem
    (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (230) CdtProblem
    (231) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (232) CdtProblem
    (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (234) CdtProblem
    (235) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (236) CdtProblem
    (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (238) CdtProblem
    (239) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (240) CdtProblem
    (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (242) CdtProblem
    (243) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (244) CdtProblem
    (245) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (246) CdtProblem
    (247) CdtRewritingProof [BOTH BOUNDS(ID, ID), 9 ms]
    (248) CdtProblem
    (249) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (250) CdtProblem
    (251) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (252) CdtProblem
    (253) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (254) CdtProblem
    (255) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (256) CdtProblem
    (257) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (258) 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:

   eq(0, 0) -> true
   eq(0, s(x)) -> false
   eq(s(x), 0) -> false
   eq(s(x), s(y)) -> eq(x, y)
   or(true, y) -> true
   or(false, y) -> y
   union(empty, h) -> h
   union(edge(x, y, i), h) -> edge(x, y, union(i, h))
   isEmpty(empty) -> true
   isEmpty(edge(x, y, i)) -> false
   from(edge(x, y, i)) -> x
   to(edge(x, y, i)) -> y
   rest(edge(x, y, i)) -> i
   rest(empty) -> empty
   reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
   if1(true, b1, b2, b3, x, y, i, h) -> true
   if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h)
   if2(true, b2, b3, x, y, i, h) -> false
   if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
   if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h))
   if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h)
   if4(true, x, y, i, h) -> true
   if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty))

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:

   eq(0', 0') -> true
   eq(0', s(x)) -> false
   eq(s(x), 0') -> false
   eq(s(x), s(y)) -> eq(x, y)
   or(true, y) -> true
   or(false, y) -> y
   union(empty, h) -> h
   union(edge(x, y, i), h) -> edge(x, y, union(i, h))
   isEmpty(empty) -> true
   isEmpty(edge(x, y, i)) -> false
   from(edge(x, y, i)) -> x
   to(edge(x, y, i)) -> y
   rest(edge(x, y, i)) -> i
   rest(empty) -> empty
   reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
   if1(true, b1, b2, b3, x, y, i, h) -> true
   if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h)
   if2(true, b2, b3, x, y, i, h) -> false
   if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
   if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h))
   if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h)
   if4(true, x, y, i, h) -> true
   if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty))

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:

   eq(0, 0) -> true
   eq(0, s(x)) -> false
   eq(s(x), 0) -> false
   eq(s(x), s(y)) -> eq(x, y)
   or(true, y) -> true
   or(false, y) -> y
   union(empty, h) -> h
   union(edge(x, y, i), h) -> edge(x, y, union(i, h))
   isEmpty(empty) -> true
   isEmpty(edge(x, y, i)) -> false
   from(edge(x, y, i)) -> x
   to(edge(x, y, i)) -> y
   rest(edge(x, y, i)) -> i
   rest(empty) -> empty
   reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
   if1(true, b1, b2, b3, x, y, i, h) -> true
   if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h)
   if2(true, b2, b3, x, y, i, h) -> false
   if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
   if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h))
   if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h)
   if4(true, x, y, i, h) -> true
   if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty))

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:

   eq(0, 0) -> true [1]
   eq(0, s(x)) -> false [1]
   eq(s(x), 0) -> false [1]
   eq(s(x), s(y)) -> eq(x, y) [1]
   or(true, y) -> true [1]
   or(false, y) -> y [1]
   union(empty, h) -> h [1]
   union(edge(x, y, i), h) -> edge(x, y, union(i, h)) [1]
   isEmpty(empty) -> true [1]
   isEmpty(edge(x, y, i)) -> false [1]
   from(edge(x, y, i)) -> x [1]
   to(edge(x, y, i)) -> y [1]
   rest(edge(x, y, i)) -> i [1]
   rest(empty) -> empty [1]
   reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) [1]
   if1(true, b1, b2, b3, x, y, i, h) -> true [1]
   if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h) [1]
   if2(true, b2, b3, x, y, i, h) -> false [1]
   if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) [1]
   if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h)) [1]
   if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h) [1]
   if4(true, x, y, i, h) -> true [1]
   if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty)) [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:

   eq(0, 0) -> true [1]
   eq(0, s(x)) -> false [1]
   eq(s(x), 0) -> false [1]
   eq(s(x), s(y)) -> eq(x, y) [1]
   or(true, y) -> true [1]
   or(false, y) -> y [1]
   union(empty, h) -> h [1]
   union(edge(x, y, i), h) -> edge(x, y, union(i, h)) [1]
   isEmpty(empty) -> true [1]
   isEmpty(edge(x, y, i)) -> false [1]
   from(edge(x, y, i)) -> x [1]
   to(edge(x, y, i)) -> y [1]
   rest(edge(x, y, i)) -> i [1]
   rest(empty) -> empty [1]
   reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) [1]
   if1(true, b1, b2, b3, x, y, i, h) -> true [1]
   if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h) [1]
   if2(true, b2, b3, x, y, i, h) -> false [1]
   if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) [1]
   if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h)) [1]
   if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h) [1]
   if4(true, x, y, i, h) -> true [1]
   if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty)) [1]

The TRS has the following type information:
eq :: 0:s -> 0:s -> true:false
0 :: 0:s
true :: true:false
s :: 0:s -> 0:s
false :: true:false
or :: true:false -> true:false -> true:false
union :: empty:edge -> empty:edge -> empty:edge
empty :: empty:edge
edge :: 0:s -> 0:s -> empty:edge -> empty:edge
isEmpty :: empty:edge -> true:false
from :: empty:edge -> 0:s
to :: empty:edge -> 0:s
rest :: empty:edge -> empty:edge
reach :: 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if1 :: true:false -> true:false -> true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if2 :: true:false -> true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if3 :: true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if4 :: true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false

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:

   eq_2
   isEmpty_1
   from_1
   to_1
   rest_1
   reach_4
   union_2
   if1_8
   if2_7
   if3_6
   if4_5
   or_2

Due to the following rules being added:

   from(v0) -> 0 [0]
   to(v0) -> 0 [0]

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:

   eq(0, 0) -> true [1]
   eq(0, s(x)) -> false [1]
   eq(s(x), 0) -> false [1]
   eq(s(x), s(y)) -> eq(x, y) [1]
   or(true, y) -> true [1]
   or(false, y) -> y [1]
   union(empty, h) -> h [1]
   union(edge(x, y, i), h) -> edge(x, y, union(i, h)) [1]
   isEmpty(empty) -> true [1]
   isEmpty(edge(x, y, i)) -> false [1]
   from(edge(x, y, i)) -> x [1]
   to(edge(x, y, i)) -> y [1]
   rest(edge(x, y, i)) -> i [1]
   rest(empty) -> empty [1]
   reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) [1]
   if1(true, b1, b2, b3, x, y, i, h) -> true [1]
   if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h) [1]
   if2(true, b2, b3, x, y, i, h) -> false [1]
   if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) [1]
   if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h)) [1]
   if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h) [1]
   if4(true, x, y, i, h) -> true [1]
   if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty)) [1]
   from(v0) -> 0 [0]
   to(v0) -> 0 [0]

The TRS has the following type information:
eq :: 0:s -> 0:s -> true:false
0 :: 0:s
true :: true:false
s :: 0:s -> 0:s
false :: true:false
or :: true:false -> true:false -> true:false
union :: empty:edge -> empty:edge -> empty:edge
empty :: empty:edge
edge :: 0:s -> 0:s -> empty:edge -> empty:edge
isEmpty :: empty:edge -> true:false
from :: empty:edge -> 0:s
to :: empty:edge -> 0:s
rest :: empty:edge -> empty:edge
reach :: 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if1 :: true:false -> true:false -> true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if2 :: true:false -> true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if3 :: true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if4 :: true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false

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:

   eq(0, 0) -> true [1]
   eq(0, s(x)) -> false [1]
   eq(s(x), 0) -> false [1]
   eq(s(x), s(y)) -> eq(x, y) [1]
   or(true, y) -> true [1]
   or(false, y) -> y [1]
   union(empty, h) -> h [1]
   union(edge(x, y, i), h) -> edge(x, y, union(i, h)) [1]
   isEmpty(empty) -> true [1]
   isEmpty(edge(x, y, i)) -> false [1]
   from(edge(x, y, i)) -> x [1]
   to(edge(x, y, i)) -> y [1]
   rest(edge(x, y, i)) -> i [1]
   rest(empty) -> empty [1]
   reach(0, 0, empty, h) -> if1(true, true, eq(0, 0), eq(0, 0), 0, 0, empty, h) [3]
   reach(0, 0, edge(x2, y'', i'), h) -> if1(true, false, eq(0, x2), eq(0, y''), 0, 0, edge(x2, y'', i'), h) [5]
   reach(0, 0, edge(x2, y'', i'), h) -> if1(true, false, eq(0, x2), eq(0, 0), 0, 0, edge(x2, y'', i'), h) [4]
   reach(0, 0, edge(x2, y'', i'), h) -> if1(true, false, eq(0, 0), eq(0, y''), 0, 0, edge(x2, y'', i'), h) [4]
   reach(0, 0, edge(x2, y'', i'), h) -> if1(true, false, eq(0, 0), eq(0, 0), 0, 0, edge(x2, y'', i'), h) [3]
   reach(0, s(x'), empty, h) -> if1(false, true, eq(0, 0), eq(s(x'), 0), 0, s(x'), empty, h) [3]
   reach(0, s(x'), edge(x3, y1, i''), h) -> if1(false, false, eq(0, x3), eq(s(x'), y1), 0, s(x'), edge(x3, y1, i''), h) [5]
   reach(0, s(x'), edge(x3, y1, i''), h) -> if1(false, false, eq(0, x3), eq(s(x'), 0), 0, s(x'), edge(x3, y1, i''), h) [4]
   reach(0, s(x'), edge(x3, y1, i''), h) -> if1(false, false, eq(0, 0), eq(s(x'), y1), 0, s(x'), edge(x3, y1, i''), h) [4]
   reach(0, s(x'), edge(x3, y1, i''), h) -> if1(false, false, eq(0, 0), eq(s(x'), 0), 0, s(x'), edge(x3, y1, i''), h) [3]
   reach(s(x''), 0, empty, h) -> if1(false, true, eq(s(x''), 0), eq(0, 0), s(x''), 0, empty, h) [3]
   reach(s(x''), 0, edge(x4, y2, i1), h) -> if1(false, false, eq(s(x''), x4), eq(0, y2), s(x''), 0, edge(x4, y2, i1), h) [5]
   reach(s(x''), 0, edge(x4, y2, i1), h) -> if1(false, false, eq(s(x''), x4), eq(0, 0), s(x''), 0, edge(x4, y2, i1), h) [4]
   reach(s(x''), 0, edge(x4, y2, i1), h) -> if1(false, false, eq(s(x''), 0), eq(0, y2), s(x''), 0, edge(x4, y2, i1), h) [4]
   reach(s(x''), 0, edge(x4, y2, i1), h) -> if1(false, false, eq(s(x''), 0), eq(0, 0), s(x''), 0, edge(x4, y2, i1), h) [3]
   reach(s(x1), s(y'), empty, h) -> if1(eq(x1, y'), true, eq(s(x1), 0), eq(s(y'), 0), s(x1), s(y'), empty, h) [3]
   reach(s(x1), s(y'), edge(x5, y3, i2), h) -> if1(eq(x1, y'), false, eq(s(x1), x5), eq(s(y'), y3), s(x1), s(y'), edge(x5, y3, i2), h) [5]
   reach(s(x1), s(y'), edge(x5, y3, i2), h) -> if1(eq(x1, y'), false, eq(s(x1), x5), eq(s(y'), 0), s(x1), s(y'), edge(x5, y3, i2), h) [4]
   reach(s(x1), s(y'), edge(x5, y3, i2), h) -> if1(eq(x1, y'), false, eq(s(x1), 0), eq(s(y'), y3), s(x1), s(y'), edge(x5, y3, i2), h) [4]
   reach(s(x1), s(y'), edge(x5, y3, i2), h) -> if1(eq(x1, y'), false, eq(s(x1), 0), eq(s(y'), 0), s(x1), s(y'), edge(x5, y3, i2), h) [3]
   if1(true, b1, b2, b3, x, y, i, h) -> true [1]
   if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h) [1]
   if2(true, b2, b3, x, y, i, h) -> false [1]
   if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) [1]
   if3(false, b3, x, y, edge(x6, y4, i3), h) -> reach(x, y, i3, edge(x6, y4, h)) [4]
   if3(false, b3, x, y, edge(x6, y4, i3), h) -> reach(x, y, i3, edge(x6, 0, h)) [3]
   if3(false, b3, x, y, edge(x6, y4, i3), h) -> reach(x, y, i3, edge(0, y4, h)) [3]
   if3(false, b3, x, y, edge(x6, y4, i3), h) -> reach(x, y, i3, edge(0, 0, h)) [2]
   if3(false, b3, x, y, empty, h) -> reach(x, y, empty, edge(0, 0, h)) [2]
   if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h) [1]
   if4(true, x, y, i, h) -> true [1]
   if4(false, x, y, edge(x7, y5, i4), h) -> or(reach(x, y, i4, h), reach(y5, y, union(i4, h), empty)) [4]
   if4(false, x, y, edge(x7, y5, i4), h) -> or(reach(x, y, i4, h), reach(0, y, union(i4, h), empty)) [3]
   if4(false, x, y, empty, h) -> or(reach(x, y, empty, h), reach(0, y, union(empty, h), empty)) [3]
   from(v0) -> 0 [0]
   to(v0) -> 0 [0]

The TRS has the following type information:
eq :: 0:s -> 0:s -> true:false
0 :: 0:s
true :: true:false
s :: 0:s -> 0:s
false :: true:false
or :: true:false -> true:false -> true:false
union :: empty:edge -> empty:edge -> empty:edge
empty :: empty:edge
edge :: 0:s -> 0:s -> empty:edge -> empty:edge
isEmpty :: empty:edge -> true:false
from :: empty:edge -> 0:s
to :: empty:edge -> 0:s
rest :: empty:edge -> empty:edge
reach :: 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if1 :: true:false -> true:false -> true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if2 :: true:false -> true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if3 :: true:false -> true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false
if4 :: true:false -> 0:s -> 0:s -> empty:edge -> empty:edge -> true:false

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
   true => 1
   false => 0
   empty => 0

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

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

   eq(z, z') -{ 1 }-> eq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' = 1 + x, x >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: x >= 0, z = 1 + x, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(b1, b2, b3, x, y, i, h) :|: z2 = x, b1 >= 0, z1 = b3, z3 = y, y >= 0, z4 = i, z5 = h, i >= 0, h >= 0, z' = b1, z = 0, z'' = b2, b3 >= 0, b2 >= 0, x >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z2 = x, b1 >= 0, z = 1, z1 = b3, z3 = y, y >= 0, z4 = i, z5 = h, i >= 0, h >= 0, z' = b1, z'' = b2, b3 >= 0, b2 >= 0, x >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(b2, b3, x, y, i, h) :|: z3 = i, z4 = h, y >= 0, i >= 0, z' = b2, h >= 0, z = 0, z'' = b3, z1 = x, b3 >= 0, b2 >= 0, z2 = y, x >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z3 = i, z4 = h, y >= 0, i >= 0, z' = b2, h >= 0, z'' = b3, z1 = x, b3 >= 0, b2 >= 0, z2 = y, x >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(x, y, i3, 1 + x6 + y4 + h) :|: z1 = y, z' = b3, y >= 0, h >= 0, y4 >= 0, z = 0, b3 >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z3 = h, x >= 0, x6 >= 0, z'' = x
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(x, y, i3, 1 + x6 + 0 + h) :|: z1 = y, z' = b3, y >= 0, h >= 0, y4 >= 0, z = 0, b3 >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z3 = h, x >= 0, x6 >= 0, z'' = x
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(x, y, i3, 1 + 0 + y4 + h) :|: z1 = y, z' = b3, y >= 0, h >= 0, y4 >= 0, z = 0, b3 >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z3 = h, x >= 0, x6 >= 0, z'' = x
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(x, y, i3, 1 + 0 + 0 + h) :|: z1 = y, z' = b3, y >= 0, h >= 0, y4 >= 0, z = 0, b3 >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z3 = h, x >= 0, x6 >= 0, z'' = x
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(x, y, 0, 1 + 0 + 0 + h) :|: z1 = y, z3 = h, z' = b3, z2 = 0, x >= 0, y >= 0, z'' = x, h >= 0, z = 0, b3 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(b3, x, y, i, h) :|: z1 = y, z2 = i, z3 = h, z' = b3, z = 1, x >= 0, y >= 0, i >= 0, z'' = x, h >= 0, b3 >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(x, y, i4, h), reach(y5, y, union(i4, h), 0)) :|: y5 >= 0, z' = x, z'' = y, x7 >= 0, x >= 0, y >= 0, h >= 0, z = 0, z2 = h, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(x, y, i4, h), reach(0, y, union(i4, h), 0)) :|: y5 >= 0, z' = x, z'' = y, x7 >= 0, x >= 0, y >= 0, h >= 0, z = 0, z2 = h, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(x, y, 0, h), reach(0, y, union(0, h), 0)) :|: z1 = 0, z' = x, z'' = y, x >= 0, y >= 0, h >= 0, z = 0, z2 = h
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0, i >= 0, h >= 0, z1 = i, z2 = h
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y
   or(z, z') -{ 1 }-> 1 :|: z = 1, y >= 0, z' = y
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(x1, y'), 1, eq(1 + x1, 0), eq(1 + y', 0), 1 + x1, 1 + y', 0, h) :|: z'' = 0, x1 >= 0, z = 1 + x1, y' >= 0, h >= 0, z' = 1 + y', z1 = h
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(x1, y'), 0, eq(1 + x1, x5), eq(1 + y', y3), 1 + x1, 1 + y', 1 + x5 + y3 + i2, h) :|: x1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z = 1 + x1, y' >= 0, y3 >= 0, h >= 0, z' = 1 + y', i2 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(x1, y'), 0, eq(1 + x1, x5), eq(1 + y', 0), 1 + x1, 1 + y', 1 + x5 + y3 + i2, h) :|: x1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z = 1 + x1, y' >= 0, y3 >= 0, h >= 0, z' = 1 + y', i2 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(x1, y'), 0, eq(1 + x1, 0), eq(1 + y', y3), 1 + x1, 1 + y', 1 + x5 + y3 + i2, h) :|: x1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z = 1 + x1, y' >= 0, y3 >= 0, h >= 0, z' = 1 + y', i2 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(x1, y'), 0, eq(1 + x1, 0), eq(1 + y', 0), 1 + x1, 1 + y', 1 + x5 + y3 + i2, h) :|: x1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z = 1 + x1, y' >= 0, y3 >= 0, h >= 0, z' = 1 + y', i2 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, h) :|: z'' = 0, h >= 0, z = 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', h) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, h >= 0, z = 0, x2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', h) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, h >= 0, z = 0, x2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', h) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, h >= 0, z = 0, x2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', h) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, h >= 0, z = 0, x2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + x', 0), 0, 1 + x', 0, h) :|: z'' = 0, z' = 1 + x', x' >= 0, h >= 0, z = 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + x'', 0), eq(0, 0), 1 + x'', 0, 0, h) :|: z = 1 + x'', z'' = 0, h >= 0, x'' >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + x', y1), 0, 1 + x', 1 + x3 + y1 + i'', h) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' = 1 + x', x' >= 0, h >= 0, z = 0, x3 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + x', 0), 0, 1 + x', 1 + x3 + y1 + i'', h) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' = 1 + x', x' >= 0, h >= 0, z = 0, x3 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + x', y1), 0, 1 + x', 1 + x3 + y1 + i'', h) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' = 1 + x', x' >= 0, h >= 0, z = 0, x3 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + x', 0), 0, 1 + x', 1 + x3 + y1 + i'', h) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' = 1 + x', x' >= 0, h >= 0, z = 0, x3 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + x'', x4), eq(0, y2), 1 + x'', 0, 1 + x4 + y2 + i1, h) :|: z = 1 + x'', x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, h >= 0, x'' >= 0, y2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + x'', x4), eq(0, 0), 1 + x'', 0, 1 + x4 + y2 + i1, h) :|: z = 1 + x'', x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, h >= 0, x'' >= 0, y2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + x'', 0), eq(0, y2), 1 + x'', 0, 1 + x4 + y2 + i1, h) :|: z = 1 + x'', x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, h >= 0, x'' >= 0, y2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + x'', 0), eq(0, 0), 1 + x'', 0, 1 + x4 + y2 + i1, h) :|: z = 1 + x'', x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, h >= 0, x'' >= 0, y2 >= 0, z' = 0, z1 = h
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   union(z, z') -{ 1 }-> h :|: z' = h, h >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, h) :|: z' = h, x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, h >= 0


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

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

   or(z, z') -{ 1 }-> 1 :|: z = 1, y >= 0, z' = y
   or(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y

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

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

   eq(z, z') -{ 1 }-> eq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' = 1 + x, x >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: x >= 0, z = 1 + x, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(b1, b2, b3, x, y, i, h) :|: z2 = x, b1 >= 0, z1 = b3, z3 = y, y >= 0, z4 = i, z5 = h, i >= 0, h >= 0, z' = b1, z = 0, z'' = b2, b3 >= 0, b2 >= 0, x >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z2 = x, b1 >= 0, z = 1, z1 = b3, z3 = y, y >= 0, z4 = i, z5 = h, i >= 0, h >= 0, z' = b1, z'' = b2, b3 >= 0, b2 >= 0, x >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(b2, b3, x, y, i, h) :|: z3 = i, z4 = h, y >= 0, i >= 0, z' = b2, h >= 0, z = 0, z'' = b3, z1 = x, b3 >= 0, b2 >= 0, z2 = y, x >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z3 = i, z4 = h, y >= 0, i >= 0, z' = b2, h >= 0, z'' = b3, z1 = x, b3 >= 0, b2 >= 0, z2 = y, x >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(x, y, i3, 1 + x6 + y4 + h) :|: z1 = y, z' = b3, y >= 0, h >= 0, y4 >= 0, z = 0, b3 >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z3 = h, x >= 0, x6 >= 0, z'' = x
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(x, y, i3, 1 + x6 + 0 + h) :|: z1 = y, z' = b3, y >= 0, h >= 0, y4 >= 0, z = 0, b3 >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z3 = h, x >= 0, x6 >= 0, z'' = x
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(x, y, i3, 1 + 0 + y4 + h) :|: z1 = y, z' = b3, y >= 0, h >= 0, y4 >= 0, z = 0, b3 >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z3 = h, x >= 0, x6 >= 0, z'' = x
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(x, y, i3, 1 + 0 + 0 + h) :|: z1 = y, z' = b3, y >= 0, h >= 0, y4 >= 0, z = 0, b3 >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z3 = h, x >= 0, x6 >= 0, z'' = x
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(x, y, 0, 1 + 0 + 0 + h) :|: z1 = y, z3 = h, z' = b3, z2 = 0, x >= 0, y >= 0, z'' = x, h >= 0, z = 0, b3 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(b3, x, y, i, h) :|: z1 = y, z2 = i, z3 = h, z' = b3, z = 1, x >= 0, y >= 0, i >= 0, z'' = x, h >= 0, b3 >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(x, y, i4, h), reach(y5, y, union(i4, h), 0)) :|: y5 >= 0, z' = x, z'' = y, x7 >= 0, x >= 0, y >= 0, h >= 0, z = 0, z2 = h, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(x, y, i4, h), reach(0, y, union(i4, h), 0)) :|: y5 >= 0, z' = x, z'' = y, x7 >= 0, x >= 0, y >= 0, h >= 0, z = 0, z2 = h, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(x, y, 0, h), reach(0, y, union(0, h), 0)) :|: z1 = 0, z' = x, z'' = y, x >= 0, y >= 0, h >= 0, z = 0, z2 = h
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0, i >= 0, h >= 0, z1 = i, z2 = h
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y
   or(z, z') -{ 1 }-> 1 :|: z = 1, y >= 0, z' = y
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(x1, y'), 1, eq(1 + x1, 0), eq(1 + y', 0), 1 + x1, 1 + y', 0, h) :|: z'' = 0, x1 >= 0, z = 1 + x1, y' >= 0, h >= 0, z' = 1 + y', z1 = h
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(x1, y'), 0, eq(1 + x1, x5), eq(1 + y', y3), 1 + x1, 1 + y', 1 + x5 + y3 + i2, h) :|: x1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z = 1 + x1, y' >= 0, y3 >= 0, h >= 0, z' = 1 + y', i2 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(x1, y'), 0, eq(1 + x1, x5), eq(1 + y', 0), 1 + x1, 1 + y', 1 + x5 + y3 + i2, h) :|: x1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z = 1 + x1, y' >= 0, y3 >= 0, h >= 0, z' = 1 + y', i2 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(x1, y'), 0, eq(1 + x1, 0), eq(1 + y', y3), 1 + x1, 1 + y', 1 + x5 + y3 + i2, h) :|: x1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z = 1 + x1, y' >= 0, y3 >= 0, h >= 0, z' = 1 + y', i2 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(x1, y'), 0, eq(1 + x1, 0), eq(1 + y', 0), 1 + x1, 1 + y', 1 + x5 + y3 + i2, h) :|: x1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z = 1 + x1, y' >= 0, y3 >= 0, h >= 0, z' = 1 + y', i2 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, h) :|: z'' = 0, h >= 0, z = 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', h) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, h >= 0, z = 0, x2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', h) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, h >= 0, z = 0, x2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', h) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, h >= 0, z = 0, x2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', h) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, h >= 0, z = 0, x2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + x', 0), 0, 1 + x', 0, h) :|: z'' = 0, z' = 1 + x', x' >= 0, h >= 0, z = 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + x'', 0), eq(0, 0), 1 + x'', 0, 0, h) :|: z = 1 + x'', z'' = 0, h >= 0, x'' >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + x', y1), 0, 1 + x', 1 + x3 + y1 + i'', h) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' = 1 + x', x' >= 0, h >= 0, z = 0, x3 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + x', 0), 0, 1 + x', 1 + x3 + y1 + i'', h) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' = 1 + x', x' >= 0, h >= 0, z = 0, x3 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + x', y1), 0, 1 + x', 1 + x3 + y1 + i'', h) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' = 1 + x', x' >= 0, h >= 0, z = 0, x3 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + x', 0), 0, 1 + x', 1 + x3 + y1 + i'', h) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' = 1 + x', x' >= 0, h >= 0, z = 0, x3 >= 0, z1 = h
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + x'', x4), eq(0, y2), 1 + x'', 0, 1 + x4 + y2 + i1, h) :|: z = 1 + x'', x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, h >= 0, x'' >= 0, y2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + x'', x4), eq(0, 0), 1 + x'', 0, 1 + x4 + y2 + i1, h) :|: z = 1 + x'', x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, h >= 0, x'' >= 0, y2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + x'', 0), eq(0, y2), 1 + x'', 0, 1 + x4 + y2 + i1, h) :|: z = 1 + x'', x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, h >= 0, x'' >= 0, y2 >= 0, z' = 0, z1 = h
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + x'', 0), eq(0, 0), 1 + x'', 0, 1 + x4 + y2 + i1, h) :|: z = 1 + x'', x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, h >= 0, x'' >= 0, y2 >= 0, z' = 0, z1 = h
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   union(z, z') -{ 1 }-> h :|: z' = h, h >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, h) :|: z' = h, x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, h >= 0


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

(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:

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0


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

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

   { to }
   { from }
   { isEmpty }
   { rest }
   { eq }
   { union }
   { or }
   { if2, if4, reach, if1, if3 }

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {to}, {from}, {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {to}, {from}, {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {to}, {from}, {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: ?, size: O(n^1) [z]

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {from}, {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {from}, {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {from}, {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: ?, size: O(n^1) [z]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {isEmpty}, {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: ?, size: O(1) [1]

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {rest}, {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: ?, size: O(n^1) [z]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {eq}, {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: ?, size: O(1) [1]

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: eq
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + z'

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

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 1, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), x5), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), y3), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(eq(z - 1, z' - 1), 0, eq(1 + (z - 1), 0), eq(1 + (z' - 1), 0), 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 1, eq(0, 0), eq(0, 0), 0, 0, 0, z1) :|: z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(1, 0, eq(0, x2), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, x2), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(1, 0, eq(0, 0), eq(0, y''), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(1, 0, eq(0, 0), eq(0, 0), 0, 0, 1 + x2 + y'' + i', z1) :|: z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 0, z1) :|: z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 1, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 0, z1) :|: z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, x3), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), y1), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(0, 0), eq(1 + (z' - 1), 0), 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 5 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), x4), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 4 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, y2), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 3 }-> if1(0, 0, eq(1 + (z - 1), 0), eq(0, 0), 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]

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

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

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

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {union}, {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]
  union: runtime: ?, size: O(n^1) [z + z']

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(56)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', i4, z2), reach(0, z'', union(i4, z2), 0)) :|: y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 3 }-> or(reach(z', z'', 0, z2), reach(0, z'', union(0, z2), 0)) :|: z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, z') :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]
  union: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']

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

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

(58)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 5 + i4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', s45, 0)) :|: s45 >= 0, s45 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 + i4 }-> or(reach(z', z'', i4, z2), reach(0, z'', s46, 0)) :|: s46 >= 0, s46 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', 0, z2), reach(0, z'', s47, 0)) :|: s47 >= 0, s47 <= 0 + z2, z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 2 + i }-> 1 + x + y + s44 :|: s44 >= 0, s44 <= i + z', x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]
  union: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(60)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 5 + i4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', s45, 0)) :|: s45 >= 0, s45 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 + i4 }-> or(reach(z', z'', i4, z2), reach(0, z'', s46, 0)) :|: s46 >= 0, s46 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', 0, z2), reach(0, z'', s47, 0)) :|: s47 >= 0, s47 <= 0 + z2, z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 2 + i }-> 1 + x + y + s44 :|: s44 >= 0, s44 <= i + z', x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {or}, {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]
  union: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  or: runtime: ?, size: O(n^1) [1 + z']

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(62)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 5 + i4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', s45, 0)) :|: s45 >= 0, s45 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 + i4 }-> or(reach(z', z'', i4, z2), reach(0, z'', s46, 0)) :|: s46 >= 0, s46 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', 0, z2), reach(0, z'', s47, 0)) :|: s47 >= 0, s47 <= 0 + z2, z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 2 + i }-> 1 + x + y + s44 :|: s44 >= 0, s44 <= i + z', x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]
  union: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  or: runtime: O(1) [1], size: O(n^1) [1 + z']

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

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

(64)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 5 + i4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', s45, 0)) :|: s45 >= 0, s45 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 + i4 }-> or(reach(z', z'', i4, z2), reach(0, z'', s46, 0)) :|: s46 >= 0, s46 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', 0, z2), reach(0, z'', s47, 0)) :|: s47 >= 0, s47 <= 0 + z2, z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 2 + i }-> 1 + x + y + s44 :|: s44 >= 0, s44 <= i + z', x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]
  union: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  or: runtime: O(1) [1], size: O(n^1) [1 + z']

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: if2
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

Computed SIZE bound using CoFloCo for: if4
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

Computed SIZE bound using CoFloCo for: if1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

Computed SIZE bound using CoFloCo for: if3
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

(66)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 5 + i4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', s45, 0)) :|: s45 >= 0, s45 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 + i4 }-> or(reach(z', z'', i4, z2), reach(0, z'', s46, 0)) :|: s46 >= 0, s46 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', 0, z2), reach(0, z'', s47, 0)) :|: s47 >= 0, s47 <= 0 + z2, z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 2 + i }-> 1 + x + y + s44 :|: s44 >= 0, s44 <= i + z', x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]
  union: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  or: runtime: O(1) [1], size: O(n^1) [1 + z']
  if2: runtime: ?, size: INF
  if4: runtime: ?, size: INF
  reach: runtime: ?, size: INF
  if1: runtime: ?, size: INF
  if3: runtime: ?, size: INF

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

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: if2
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

(68)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 3 + z' }-> s :|: s >= 0, s <= 1, z - 1 >= 0, z' - 1 >= 0
   eq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: z >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(z', z'', z1, z2, z3, z4, z5) :|: z' >= 0, z3 >= 0, z4 >= 0, z5 >= 0, z = 0, z1 >= 0, z'' >= 0, z2 >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 1 :|: z' >= 0, z = 1, z3 >= 0, z4 >= 0, z5 >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(z', z'', z1, z2, z3, z4) :|: z2 >= 0, z3 >= 0, z4 >= 0, z = 0, z'' >= 0, z' >= 0, z1 >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 1, z2 >= 0, z3 >= 0, z4 >= 0, z'' >= 0, z' >= 0, z1 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 4 }-> reach(z'', z1, i3, 1 + x6 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + x6 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 3 }-> reach(z'', z1, i3, 1 + 0 + y4 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, i3, 1 + 0 + 0 + z3) :|: z1 >= 0, z3 >= 0, y4 >= 0, z = 0, z' >= 0, i3 >= 0, z2 = 1 + x6 + y4 + i3, z'' >= 0, x6 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 2 }-> reach(z'', z1, 0, 1 + 0 + 0 + z3) :|: z2 = 0, z'' >= 0, z1 >= 0, z3 >= 0, z = 0, z' >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(z', z'', z1, z2, z3) :|: z = 1, z'' >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z' >= 0
   if4(z, z', z'', z1, z2) -{ 5 + i4 }-> or(reach(z', z'', i4, z2), reach(y5, z'', s45, 0)) :|: s45 >= 0, s45 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 + i4 }-> or(reach(z', z'', i4, z2), reach(0, z'', s46, 0)) :|: s46 >= 0, s46 <= i4 + z2, y5 >= 0, x7 >= 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0, i4 >= 0, z1 = 1 + x7 + y5 + i4
   if4(z, z', z'', z1, z2) -{ 4 }-> or(reach(z', z'', 0, z2), reach(0, z'', s47, 0)) :|: s47 >= 0, s47 <= 0 + z2, z1 = 0, z' >= 0, z'' >= 0, z2 >= 0, z = 0
   if4(z, z', z'', z1, z2) -{ 1 }-> 1 :|: z = 1, z' >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   isEmpty(z) -{ 1 }-> 1 :|: z = 0
   isEmpty(z) -{ 1 }-> 0 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   or(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s29, 1, s30, s31, 1 + (z - 1), 1 + (z' - 1), 0, z1) :|: s29 >= 0, s29 <= 1, s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 1, z'' = 0, z - 1 >= 0, z' - 1 >= 0, z1 >= 0
   reach(z, z', z'', z1) -{ 13 + x5 + y3 + z' }-> if1(s32, 0, s33, s34, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s32 >= 0, s32 <= 1, s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + x5 + z' }-> if1(s35, 0, s36, s37, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s35 >= 0, s35 <= 1, s36 >= 0, s36 <= 1, s37 >= 0, s37 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 12 + y3 + z' }-> if1(s38, 0, s39, s40, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 1, s40 >= 0, s40 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 11 + z' }-> if1(s41, 0, s42, s43, 1 + (z - 1), 1 + (z' - 1), 1 + x5 + y3 + i2, z1) :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 1, z - 1 >= 0, x5 >= 0, z'' = 1 + x5 + y3 + i2, z' - 1 >= 0, y3 >= 0, z1 >= 0, i2 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 1, s', s'', 0, 0, 0, z1) :|: s' >= 0, s' <= 1, s'' >= 0, s'' <= 1, z'' = 0, z1 >= 0, z = 0, z' = 0
   reach(z, z', z'', z1) -{ 11 + x2 + y'' }-> if1(1, 0, s1, s2, 0, 0, 1 + x2 + y'' + i', z1) :|: s1 >= 0, s1 <= 1, s2 >= 0, s2 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x2 }-> if1(1, 0, s3, s4, 0, 0, 1 + x2 + y'' + i', z1) :|: s3 >= 0, s3 <= 1, s4 >= 0, s4 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y'' }-> if1(1, 0, s5, s6, 0, 0, 1 + x2 + y'' + i', z1) :|: s5 >= 0, s5 <= 1, s6 >= 0, s6 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(1, 0, s7, s8, 0, 0, 1 + x2 + y'' + i', z1) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, z'' = 1 + x2 + y'' + i', i' >= 0, y'' >= 0, z1 >= 0, z = 0, x2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s19, s20, 1 + (z - 1), 0, 0, z1) :|: s19 >= 0, s19 <= 1, s20 >= 0, s20 <= 1, z'' = 0, z1 >= 0, z - 1 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 1, s9, s10, 0, 1 + (z' - 1), 0, z1) :|: s9 >= 0, s9 <= 1, s10 >= 0, s10 <= 1, z'' = 0, z' - 1 >= 0, z1 >= 0, z = 0
   reach(z, z', z'', z1) -{ 11 + x3 + y1 }-> if1(0, 0, s11, s12, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s11 >= 0, s11 <= 1, s12 >= 0, s12 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + x3 }-> if1(0, 0, s13, s14, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 10 + y1 }-> if1(0, 0, s15, s16, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s15 >= 0, s15 <= 1, s16 >= 0, s16 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s17, s18, 0, 1 + (z' - 1), 1 + x3 + y1 + i'', z1) :|: s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 1, y1 >= 0, i'' >= 0, z'' = 1 + x3 + y1 + i'', z' - 1 >= 0, z1 >= 0, z = 0, x3 >= 0
   reach(z, z', z'', z1) -{ 11 + x4 + y2 }-> if1(0, 0, s21, s22, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + x4 }-> if1(0, 0, s23, s24, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s23 >= 0, s23 <= 1, s24 >= 0, s24 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 10 + y2 }-> if1(0, 0, s25, s26, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   reach(z, z', z'', z1) -{ 9 }-> if1(0, 0, s27, s28, 1 + (z - 1), 0, 1 + x4 + y2 + i1, z1) :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, x4 >= 0, i1 >= 0, z'' = 1 + x4 + y2 + i1, z1 >= 0, z - 1 >= 0, y2 >= 0, z' = 0
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: z >= 0
   union(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   union(z, z') -{ 2 + i }-> 1 + x + y + s44 :|: s44 >= 0, s44 <= i + z', x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, z' >= 0

Function symbols to be analyzed: {if2,if4,reach,if1,if3}
Previous analysis results are:
  to: runtime: O(1) [1], size: O(n^1) [z]
  from: runtime: O(1) [1], size: O(n^1) [z]
  isEmpty: runtime: O(1) [1], size: O(1) [1]
  rest: runtime: O(1) [1], size: O(n^1) [z]
  eq: runtime: O(n^1) [3 + z'], size: O(1) [1]
  union: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  or: runtime: O(1) [1], size: O(n^1) [1 + z']
  if2: runtime: INF, size: INF
  if4: runtime: ?, size: INF
  reach: runtime: ?, size: INF
  if1: runtime: ?, size: INF
  if3: runtime: ?, size: INF

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

(69) 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:

   from(v0) -> null_from [0]
   to(v0) -> null_to [0]
   eq(v0, v1) -> null_eq [0]
   or(v0, v1) -> null_or [0]
   if1(v0, v1, v2, v3, v4, v5, v6, v7) -> null_if1 [0]
   if2(v0, v1, v2, v3, v4, v5, v6) -> null_if2 [0]
   if3(v0, v1, v2, v3, v4, v5) -> null_if3 [0]
   if4(v0, v1, v2, v3, v4) -> null_if4 [0]

And the following fresh constants:    null_from, null_to, null_eq, null_or, null_if1, null_if2, null_if3, null_if4

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

(70)
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:

   eq(0, 0) -> true [1]
   eq(0, s(x)) -> false [1]
   eq(s(x), 0) -> false [1]
   eq(s(x), s(y)) -> eq(x, y) [1]
   or(true, y) -> true [1]
   or(false, y) -> y [1]
   union(empty, h) -> h [1]
   union(edge(x, y, i), h) -> edge(x, y, union(i, h)) [1]
   isEmpty(empty) -> true [1]
   isEmpty(edge(x, y, i)) -> false [1]
   from(edge(x, y, i)) -> x [1]
   to(edge(x, y, i)) -> y [1]
   rest(edge(x, y, i)) -> i [1]
   rest(empty) -> empty [1]
   reach(x, y, i, h) -> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) [1]
   if1(true, b1, b2, b3, x, y, i, h) -> true [1]
   if1(false, b1, b2, b3, x, y, i, h) -> if2(b1, b2, b3, x, y, i, h) [1]
   if2(true, b2, b3, x, y, i, h) -> false [1]
   if2(false, b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) [1]
   if3(false, b3, x, y, i, h) -> reach(x, y, rest(i), edge(from(i), to(i), h)) [1]
   if3(true, b3, x, y, i, h) -> if4(b3, x, y, i, h) [1]
   if4(true, x, y, i, h) -> true [1]
   if4(false, x, y, i, h) -> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), empty)) [1]
   from(v0) -> null_from [0]
   to(v0) -> null_to [0]
   eq(v0, v1) -> null_eq [0]
   or(v0, v1) -> null_or [0]
   if1(v0, v1, v2, v3, v4, v5, v6, v7) -> null_if1 [0]
   if2(v0, v1, v2, v3, v4, v5, v6) -> null_if2 [0]
   if3(v0, v1, v2, v3, v4, v5) -> null_if3 [0]
   if4(v0, v1, v2, v3, v4) -> null_if4 [0]

The TRS has the following type information:
eq :: 0:s:null_from:null_to -> 0:s:null_from:null_to -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
0 :: 0:s:null_from:null_to
true :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
s :: 0:s:null_from:null_to -> 0:s:null_from:null_to
false :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
or :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
union :: empty:edge -> empty:edge -> empty:edge
empty :: empty:edge
edge :: 0:s:null_from:null_to -> 0:s:null_from:null_to -> empty:edge -> empty:edge
isEmpty :: empty:edge -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
from :: empty:edge -> 0:s:null_from:null_to
to :: empty:edge -> 0:s:null_from:null_to
rest :: empty:edge -> empty:edge
reach :: 0:s:null_from:null_to -> 0:s:null_from:null_to -> empty:edge -> empty:edge -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
if1 :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> 0:s:null_from:null_to -> 0:s:null_from:null_to -> empty:edge -> empty:edge -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
if2 :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> 0:s:null_from:null_to -> 0:s:null_from:null_to -> empty:edge -> empty:edge -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
if3 :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> 0:s:null_from:null_to -> 0:s:null_from:null_to -> empty:edge -> empty:edge -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
if4 :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4 -> 0:s:null_from:null_to -> 0:s:null_from:null_to -> empty:edge -> empty:edge -> true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
null_from :: 0:s:null_from:null_to
null_to :: 0:s:null_from:null_to
null_eq :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
null_or :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
null_if1 :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
null_if2 :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
null_if3 :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4
null_if4 :: true:false:null_eq:null_or:null_if1:null_if2:null_if3:null_if4

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

(71) 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
   true => 2
   false => 1
   empty => 0
   null_from => 0
   null_to => 0
   null_eq => 0
   null_or => 0
   null_if1 => 0
   null_if2 => 0
   null_if3 => 0
   null_if4 => 0

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

(72)
Obligation:
Complexity RNTS consisting of the following rules:

   eq(z, z') -{ 1 }-> eq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   eq(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 1 :|: z' = 1 + x, x >= 0, z = 0
   eq(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0
   eq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   from(z) -{ 1 }-> x :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   from(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> if2(b1, b2, b3, x, y, i, h) :|: z2 = x, b1 >= 0, z = 1, z1 = b3, z3 = y, y >= 0, z4 = i, z5 = h, i >= 0, h >= 0, z' = b1, z'' = b2, b3 >= 0, b2 >= 0, x >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 1 }-> 2 :|: z2 = x, b1 >= 0, z1 = b3, z3 = y, y >= 0, z4 = i, z5 = h, i >= 0, h >= 0, z' = b1, z'' = b2, b3 >= 0, z = 2, b2 >= 0, x >= 0
   if1(z, z', z'', z1, z2, z3, z4, z5) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z5 = v7, v6 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0, z3 = v5, v4 >= 0, v7 >= 0, z4 = v6
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> if3(b2, b3, x, y, i, h) :|: z = 1, z3 = i, z4 = h, y >= 0, i >= 0, z' = b2, h >= 0, z'' = b3, z1 = x, b3 >= 0, b2 >= 0, z2 = y, x >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z3 = i, z4 = h, y >= 0, i >= 0, z' = b2, h >= 0, z'' = b3, z1 = x, b3 >= 0, z = 2, b2 >= 0, z2 = y, x >= 0
   if2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v6 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0, z3 = v5, v4 >= 0, z4 = v6
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> reach(x, y, rest(i), 1 + from(i) + to(i) + h) :|: z1 = y, z2 = i, z3 = h, z' = b3, z = 1, x >= 0, y >= 0, i >= 0, z'' = x, h >= 0, b3 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 1 }-> if4(b3, x, y, i, h) :|: z = 2, z1 = y, z2 = i, z3 = h, z' = b3, x >= 0, y >= 0, i >= 0, z'' = x, h >= 0, b3 >= 0
   if3(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z1 = v3, z3 = v5, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0
   if4(z, z', z'', z1, z2) -{ 1 }-> or(reach(x, y, rest(i), h), reach(to(i), y, union(rest(i), h), 0)) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0, i >= 0, h >= 0, z1 = i, z2 = h
   if4(z, z', z'', z1, z2) -{ 1 }-> 2 :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0, i >= 0, h >= 0, z1 = i, z2 = h
   if4(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0
   isEmpty(z) -{ 1 }-> 2 :|: z = 0
   isEmpty(z) -{ 1 }-> 1 :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   or(z, z') -{ 1 }-> y :|: z = 1, y >= 0, z' = y
   or(z, z') -{ 1 }-> 2 :|: z = 2, y >= 0, z' = y
   or(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   reach(z, z', z'', z1) -{ 1 }-> if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) :|: z'' = i, x >= 0, y >= 0, i >= 0, h >= 0, z = x, z' = y, z1 = h
   rest(z) -{ 1 }-> i :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   rest(z) -{ 1 }-> 0 :|: z = 0
   to(z) -{ 1 }-> y :|: x >= 0, y >= 0, z = 1 + x + y + i, i >= 0
   to(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   union(z, z') -{ 1 }-> h :|: z' = h, h >= 0, z = 0
   union(z, z') -{ 1 }-> 1 + x + y + union(i, h) :|: z' = h, x >= 0, y >= 0, z = 1 + x + y + i, i >= 0, h >= 0

Only complete derivations are relevant for the runtime complexity.

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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   or(true, z0) -> true
   or(false, z0) -> z0
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   reach(z0, z1, z2, z3) -> if1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3)
   if1(true, z0, z1, z2, z3, z4, z5, z6) -> true
   if1(false, z0, z1, z2, z3, z4, z5, z6) -> if2(z0, z1, z2, z3, z4, z5, z6)
   if2(true, z0, z1, z2, z3, z4, z5) -> false
   if2(false, z0, z1, z2, z3, z4, z5) -> if3(z0, z1, z2, z3, z4, z5)
   if3(false, z0, z1, z2, z3, z4) -> reach(z1, z2, rest(z3), edge(from(z3), to(z3), z4))
   if3(true, z0, z1, z2, z3, z4) -> if4(z0, z1, z2, z3, z4)
   if4(true, z0, z1, z2, z3) -> true
   if4(false, z0, z1, z2, z3) -> or(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty))
Tuples:
   EQ(0, 0) -> c
   EQ(0, s(z0)) -> c1
   EQ(s(z0), 0) -> c2
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   OR(true, z0) -> c4
   OR(false, z0) -> c5
   UNION(empty, z0) -> c6
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   ISEMPTY(empty) -> c8
   ISEMPTY(edge(z0, z1, z2)) -> c9
   FROM(edge(z0, z1, z2)) -> c10
   TO(edge(z0, z1, z2)) -> c11
   REST(edge(z0, z1, z2)) -> c12
   REST(empty) -> c13
   REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), ISEMPTY(z2))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)), FROM(z2))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)), TO(z2))
   IF1(true, z0, z1, z2, z3, z4, z5, z6) -> c18
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(true, z0, z1, z2, z3, z4, z5) -> c20
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), REST(z3))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), FROM(z3))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), TO(z3))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF4(true, z0, z1, z2, z3) -> c26
   IF4(false, z0, z1, z2, z3) -> c27(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(z0, z1, rest(z2), z3), REST(z2))
   IF4(false, z0, z1, z2, z3) -> c28(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(to(z2), z1, union(rest(z2), z3), empty), TO(z2))
   IF4(false, z0, z1, z2, z3) -> c29(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3), REST(z2))
S tuples:
   EQ(0, 0) -> c
   EQ(0, s(z0)) -> c1
   EQ(s(z0), 0) -> c2
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   OR(true, z0) -> c4
   OR(false, z0) -> c5
   UNION(empty, z0) -> c6
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   ISEMPTY(empty) -> c8
   ISEMPTY(edge(z0, z1, z2)) -> c9
   FROM(edge(z0, z1, z2)) -> c10
   TO(edge(z0, z1, z2)) -> c11
   REST(edge(z0, z1, z2)) -> c12
   REST(empty) -> c13
   REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), ISEMPTY(z2))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)), FROM(z2))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)), TO(z2))
   IF1(true, z0, z1, z2, z3, z4, z5, z6) -> c18
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(true, z0, z1, z2, z3, z4, z5) -> c20
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), REST(z3))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), FROM(z3))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), TO(z3))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF4(true, z0, z1, z2, z3) -> c26
   IF4(false, z0, z1, z2, z3) -> c27(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(z0, z1, rest(z2), z3), REST(z2))
   IF4(false, z0, z1, z2, z3) -> c28(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(to(z2), z1, union(rest(z2), z3), empty), TO(z2))
   IF4(false, z0, z1, z2, z3) -> c29(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3), REST(z2))
K tuples:none
Defined Rule Symbols:   eq_2, or_2, union_2, isEmpty_1, from_1, to_1, rest_1, reach_4, if1_8, if2_7, if3_6, if4_5

Defined Pair Symbols:   EQ_2, OR_2, UNION_2, ISEMPTY_1, FROM_1, TO_1, REST_1, REACH_4, IF1_8, IF2_7, IF3_6, IF4_5

Compound Symbols:   c, c1, c2, c3_1, c4, c5, c6, c7_1, c8, c9, c10, c11, c12, c13, c14_2, c15_2, c16_3, c17_3, c18, c19_1, c20, c21_1, c22_2, c23_2, c24_2, c25_1, c26, c27_3, c28_3, c29_4


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

(75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 15 trailing nodes:
   FROM(edge(z0, z1, z2)) -> c10
   ISEMPTY(empty) -> c8
   OR(true, z0) -> c4
   EQ(0, 0) -> c
   TO(edge(z0, z1, z2)) -> c11
   IF4(true, z0, z1, z2, z3) -> c26
   UNION(empty, z0) -> c6
   OR(false, z0) -> c5
   EQ(s(z0), 0) -> c2
   EQ(0, s(z0)) -> c1
   IF1(true, z0, z1, z2, z3, z4, z5, z6) -> c18
   REST(empty) -> c13
   IF2(true, z0, z1, z2, z3, z4, z5) -> c20
   ISEMPTY(edge(z0, z1, z2)) -> c9
   REST(edge(z0, z1, z2)) -> c12

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   or(true, z0) -> true
   or(false, z0) -> z0
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   reach(z0, z1, z2, z3) -> if1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3)
   if1(true, z0, z1, z2, z3, z4, z5, z6) -> true
   if1(false, z0, z1, z2, z3, z4, z5, z6) -> if2(z0, z1, z2, z3, z4, z5, z6)
   if2(true, z0, z1, z2, z3, z4, z5) -> false
   if2(false, z0, z1, z2, z3, z4, z5) -> if3(z0, z1, z2, z3, z4, z5)
   if3(false, z0, z1, z2, z3, z4) -> reach(z1, z2, rest(z3), edge(from(z3), to(z3), z4))
   if3(true, z0, z1, z2, z3, z4) -> if4(z0, z1, z2, z3, z4)
   if4(true, z0, z1, z2, z3) -> true
   if4(false, z0, z1, z2, z3) -> or(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), ISEMPTY(z2))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)), FROM(z2))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)), TO(z2))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), REST(z3))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), FROM(z3))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), TO(z3))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF4(false, z0, z1, z2, z3) -> c27(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(z0, z1, rest(z2), z3), REST(z2))
   IF4(false, z0, z1, z2, z3) -> c28(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(to(z2), z1, union(rest(z2), z3), empty), TO(z2))
   IF4(false, z0, z1, z2, z3) -> c29(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3), REST(z2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), ISEMPTY(z2))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)), FROM(z2))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)), TO(z2))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), REST(z3))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), FROM(z3))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)), TO(z3))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF4(false, z0, z1, z2, z3) -> c27(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(z0, z1, rest(z2), z3), REST(z2))
   IF4(false, z0, z1, z2, z3) -> c28(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(to(z2), z1, union(rest(z2), z3), empty), TO(z2))
   IF4(false, z0, z1, z2, z3) -> c29(OR(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty)), REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3), REST(z2))
K tuples:none
Defined Rule Symbols:   eq_2, or_2, union_2, isEmpty_1, from_1, to_1, rest_1, reach_4, if1_8, if2_7, if3_6, if4_5

Defined Pair Symbols:   EQ_2, UNION_2, REACH_4, IF1_8, IF2_7, IF3_6, IF4_5

Compound Symbols:   c3_1, c7_1, c14_2, c15_2, c16_3, c17_3, c19_1, c21_1, c22_2, c23_2, c24_2, c25_1, c27_3, c28_3, c29_4


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

(77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing tuple parts
----------------------------------------

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   or(true, z0) -> true
   or(false, z0) -> z0
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   reach(z0, z1, z2, z3) -> if1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3)
   if1(true, z0, z1, z2, z3, z4, z5, z6) -> true
   if1(false, z0, z1, z2, z3, z4, z5, z6) -> if2(z0, z1, z2, z3, z4, z5, z6)
   if2(true, z0, z1, z2, z3, z4, z5) -> false
   if2(false, z0, z1, z2, z3, z4, z5) -> if3(z0, z1, z2, z3, z4, z5)
   if3(false, z0, z1, z2, z3, z4) -> reach(z1, z2, rest(z3), edge(from(z3), to(z3), z4))
   if3(true, z0, z1, z2, z3, z4) -> if4(z0, z1, z2, z3, z4)
   if4(true, z0, z1, z2, z3) -> true
   if4(false, z0, z1, z2, z3) -> or(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
K tuples:none
Defined Rule Symbols:   eq_2, or_2, union_2, isEmpty_1, from_1, to_1, rest_1, reach_4, if1_8, if2_7, if3_6, if4_5

Defined Pair Symbols:   EQ_2, UNION_2, REACH_4, IF1_8, IF2_7, IF3_6, IF4_5

Compound Symbols:   c3_1, c7_1, c14_2, c19_1, c21_1, c25_1, c15_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2


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

(79) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   or(true, z0) -> true
   or(false, z0) -> z0
   reach(z0, z1, z2, z3) -> if1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3)
   if1(true, z0, z1, z2, z3, z4, z5, z6) -> true
   if1(false, z0, z1, z2, z3, z4, z5, z6) -> if2(z0, z1, z2, z3, z4, z5, z6)
   if2(true, z0, z1, z2, z3, z4, z5) -> false
   if2(false, z0, z1, z2, z3, z4, z5) -> if3(z0, z1, z2, z3, z4, z5)
   if3(false, z0, z1, z2, z3, z4) -> reach(z1, z2, rest(z3), edge(from(z3), to(z3), z4))
   if3(true, z0, z1, z2, z3, z4) -> if4(z0, z1, z2, z3, z4)
   if4(true, z0, z1, z2, z3) -> true
   if4(false, z0, z1, z2, z3) -> or(reach(z0, z1, rest(z2), z3), reach(to(z2), z1, union(rest(z2), z3), empty))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
K tuples:none
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, REACH_4, IF1_8, IF2_7, IF3_6, IF4_5

Compound Symbols:   c3_1, c7_1, c14_2, c19_1, c21_1, c25_1, c15_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(z0, z1, z2, z3) -> c14(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, z1)) by 
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(0, 0, x2, x3) -> c14(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, 0))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, s(z0)))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), 0))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(0, 0, x2, x3) -> c14(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, 0))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, s(z0)))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), 0))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(0, 0, x2, x3) -> c14(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, 0))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, s(z0)))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), 0))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
K tuples:none
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c15_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, x2, x3) -> c14(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, 0))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, s(z0)))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), 0))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, s(z0)))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), 0))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
K tuples:none
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c15_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
K tuples:none
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c15_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1


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

(87) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
We considered the (Usable) Rules:
   isEmpty(edge(z0, z1, z2)) -> false
   isEmpty(empty) -> true
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_2
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_1
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = [1]
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = [1]
   POL(REACH(x_1, x_2, x_3, x_4)) = [1]
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = [1]
   POL(from(x_1)) = 0
   POL(isEmpty(x_1)) = [1]
   POL(rest(x_1)) = [1] + x_1
   POL(s(x_1)) = x_1
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c15_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(z0, z1, z2, z3) -> c15(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3)) by 
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, 0, x2, x3) -> c15(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, 0, x2, x3) -> c15(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, 0, x2, x3) -> c15(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1


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

(91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, x2, x3) -> c15(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1


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

(93) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
We considered the (Usable) Rules:
   isEmpty(edge(z0, z1, z2)) -> false
   isEmpty(empty) -> true
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_2
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_1
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = [1]
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = [1]
   POL(REACH(x_1, x_2, x_3, x_4)) = [1]
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = x_2 + x_3
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = [1]
   POL(from(x_1)) = x_1
   POL(isEmpty(x_1)) = [1]
   POL(rest(x_1)) = [1] + x_1
   POL(s(x_1)) = x_1
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2)))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c16_2, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(z0, z1, z2, z3) -> c16(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z0, from(z2))) by 
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, from(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, x2, x3) -> c16(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, from(x2)))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, from(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, x2, x3) -> c16(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, from(x2)))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, from(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, x2, x3) -> c16(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, from(x2)))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1, c16_2


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

(97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, x2, x3) -> c16(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, from(x2)))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, from(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, from(x2)))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, from(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(0, from(x2)))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1, c16_2


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

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1, c16_2, c16_1


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

(101) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
We considered the (Usable) Rules:
   isEmpty(edge(z0, z1, z2)) -> false
   isEmpty(empty) -> true
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_2
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_1
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = [1]
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = [1]
   POL(REACH(x_1, x_2, x_3, x_4)) = [1]
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = [1]
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1]
   POL(rest(x_1)) = [1] + x_1
   POL(s(x_1)) = x_1
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2)))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, REACH_4, IF4_5

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c17_2, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1, c16_2, c16_1


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(z0, z1, z2, z3) -> c17(IF1(eq(z0, z1), isEmpty(z2), eq(z0, from(z2)), eq(z1, to(z2)), z0, z1, z2, z3), EQ(z1, to(z2))) by 
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x1, to(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, x2, x3) -> c17(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, to(x2)))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(0, to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x1, to(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, x2, x3) -> c17(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, to(x2)))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(0, to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x1, to(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, x2, x3) -> c17(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, to(x2)))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(0, to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2


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

(105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, x2, x3) -> c17(IF1(true, isEmpty(x2), eq(0, from(x2)), eq(0, to(x2)), 0, 0, x2, x3), EQ(0, to(x2)))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x1, to(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(0, to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x1, to(empty)))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(0, to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2


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

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1


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

(109) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
We considered the (Usable) Rules:
   isEmpty(edge(z0, z1, z2)) -> false
   isEmpty(empty) -> true
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_2 + x_6
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_1 + x_5
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = [1] + x_4
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = [1] + x_3
   POL(REACH(x_1, x_2, x_3, x_4)) = [1] + x_2
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1)) = x_1
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = [1]
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1]
   POL(rest(x_1)) = [1] + x_1
   POL(s(x_1)) = [1] + x_1
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c28_1, c29_2, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF4(false, z0, z1, z2, z3) -> c28(REACH(to(z2), z1, union(rest(z2), z3), empty)) by 
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c29_2, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF4(false, z0, z1, z2, z3) -> c29(REACH(to(z2), z1, union(rest(z2), z3), empty), UNION(rest(z2), z3)) by 
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1)) by 
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, 0))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, 0))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, 0))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, 0))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, 0))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, 0))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, 0))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, 0))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, 0))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, 0))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1)) by 
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, x1))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, x1))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, x1))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, x1))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, x1))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, x1))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, x1))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, x1))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, x1))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, x1))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1)) by 
   REACH(0, 0, empty, x2) -> c14(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2), EQ(0, 0))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2), EQ(0, s(z0)))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2), EQ(s(z0), 0))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, 0, empty, x2) -> c14(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2), EQ(0, 0))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2), EQ(0, s(z0)))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2), EQ(s(z0), 0))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c14(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3), EQ(x0, x1))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, empty, x2) -> c14(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2), EQ(0, 0))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2), EQ(0, s(z0)))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2), EQ(s(z0), 0))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, x1)) by 
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c14(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, 0))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, s(z0)))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), 0))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1)))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_2, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(s(z0), s(z1), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), s(z1))) by 
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(s(x1), z1), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x0), s(x1)))
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(s(x0), z0), eq(s(x1), to(edge(z0, z1, z2))), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x0), s(x1)))
   REACH(s(x0), s(x1), empty, x3) -> c14(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x0), s(x1)))
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c14(IF1(eq(x0, x1), false, eq(s(x0), from(edge(z0, z1, z2))), eq(s(x1), to(edge(z0, z1, z2))), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), s(0)))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(0), x2, x3) -> c14(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), s(0)))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(x0), s(x1), empty, x3) -> c14(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), s(0)))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(x0), s(x1), empty, x3) -> c14(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x0), s(x1)))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(143) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
We considered the (Usable) Rules:none
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_6
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_5
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = x_4
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = x_3
   POL(REACH(x_1, x_2, x_3, x_4)) = x_2
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1)) = x_1
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = 0
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1] + x_1
   POL(rest(x_1)) = 0
   POL(s(x_1)) = [1]
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(x0), s(x1), empty, x3) -> c14(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x0), s(x1)))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(145) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
We considered the (Usable) Rules:
   isEmpty(edge(z0, z1, z2)) -> false
   isEmpty(empty) -> true
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_2
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_1
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = [1]
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = [1]
   POL(REACH(x_1, x_2, x_3, x_4)) = [1]
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1)) = x_1
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = [1]
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1]
   POL(rest(x_1)) = 0
   POL(s(x_1)) = 0
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3)) by 
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3)) by 
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(155) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3)) by 
   REACH(0, 0, empty, x2) -> c15(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, 0, empty, x2) -> c15(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c15(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, empty, x2) -> c15(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(159) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3)) by 
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c15(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(163) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(s(z0), s(z1), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3)) by 
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(s(x1), z1), s(x0), s(x1), edge(z0, z1, z2), x3))
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(s(x0), z0), eq(s(x1), to(edge(z0, z1, z2))), s(x0), s(x1), edge(z0, z1, z2), x3))
   REACH(s(x0), s(x1), empty, x3) -> c15(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c15(IF1(eq(x0, x1), false, eq(s(x0), from(edge(z0, z1, z2))), eq(s(x1), to(edge(z0, z1, z2))), s(x0), s(x1), edge(z0, z1, z2), x3))
   REACH(s(0), s(0), x2, x3) -> c15(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(0), x2, x3) -> c15(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(x0), s(x1), empty, x3) -> c15(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c15(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(165) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(s(0), s(0), x2, x3) -> c15(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(x0), s(x1), empty, x3) -> c15(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(167) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
We considered the (Usable) Rules:
   isEmpty(edge(z0, z1, z2)) -> false
   isEmpty(empty) -> true
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_2
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_1
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = [1]
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = [1]
   POL(REACH(x_1, x_2, x_3, x_4)) = [1]
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1)) = x_1
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = [1]
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1]
   POL(rest(x_1)) = 0
   POL(s(x_1)) = 0
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2)))) by 
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(175) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2)))) by 
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, from(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, from(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, from(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, from(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, from(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, from(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, from(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, from(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(0, from(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(0, from(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(181) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x0, from(edge(z0, z1, z2)))) by 
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(183) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c16(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(0, from(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(187) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(s(z0), 0, x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3), EQ(s(z0), from(x2))) by 
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2)))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_2, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2


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

(189) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(s(z0), s(z1), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z0), from(x2))) by 
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(s(x1), z1), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x0), from(edge(z0, z1, z2))))
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(s(x0), z0), eq(s(x1), to(edge(z0, z1, z2))), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x0), from(edge(z0, z1, z2))))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x0), from(empty)))
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c16(IF1(eq(x0, x1), false, eq(s(x0), from(edge(z0, z1, z2))), eq(s(x1), to(edge(z0, z1, z2))), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x0), from(edge(z0, z1, z2))))
   REACH(s(0), s(0), x2, x3) -> c16(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), from(x2)))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x0), from(empty)))
   REACH(s(0), s(0), x2, x3) -> c16(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), from(x2)))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x0), from(empty)))
   REACH(s(0), s(0), x2, x3) -> c16(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), from(x2)))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(193) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
We considered the (Usable) Rules:none
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_6
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_5
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = x_4
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = x_3
   POL(REACH(x_1, x_2, x_3, x_4)) = x_2
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1)) = x_1
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = 0
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1] + x_1
   POL(rest(x_1)) = 0
   POL(s(x_1)) = [1] + x_1
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(195) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
We considered the (Usable) Rules:
   isEmpty(edge(z0, z1, z2)) -> false
   isEmpty(empty) -> true
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_2
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_1
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = [1]
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = [1]
   POL(REACH(x_1, x_2, x_3, x_4)) = [1]
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1)) = x_1
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = [1]
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1]
   POL(rest(x_1)) = 0
   POL(s(x_1)) = 0
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(197) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3)) by 
   REACH(0, 0, empty, x2) -> c16(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c16(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, 0, empty, x2) -> c16(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c16(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, empty, x2) -> c16(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(201) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2)))) by 
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(0, to(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(0, to(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(0, to(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(0, to(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(0, to(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(0, to(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(203) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(0, x3), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(0, to(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(0, to(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(0, to(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(0, to(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

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

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(207) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2)))) by 
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(209) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(213) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x3), EQ(x1, to(edge(z0, z1, z2)))) by 
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))

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

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(215) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, edge(x2, x3, x4), x5) -> c17(IF1(true, false, eq(0, from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), 0, 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))

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

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(0, to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

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

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2)))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(219) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(0, s(z0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3), EQ(s(z0), to(x2))) by 
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))

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

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2)))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_2, c17_1, c28_1, c29_2, c14_2, c16_2


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

(221) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(s(z0), s(z1), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(z0), from(x2)), eq(s(z1), to(x2)), s(z0), s(z1), x2, x3), EQ(s(z1), to(x2))) by 
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(s(x1), z1), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x1), to(edge(z0, z1, z2))))
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(s(x0), z0), eq(s(x1), to(edge(z0, z1, z2))), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x1), to(edge(z0, z1, z2))))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x1), to(empty)))
   REACH(s(x0), s(x1), edge(z0, z1, z2), x3) -> c17(IF1(eq(x0, x1), false, eq(s(x0), from(edge(z0, z1, z2))), eq(s(x1), to(edge(z0, z1, z2))), s(x0), s(x1), edge(z0, z1, z2), x3), EQ(s(x1), to(edge(z0, z1, z2))))
   REACH(s(0), s(0), x2, x3) -> c17(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))

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

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x1), to(empty)))
   REACH(s(0), s(0), x2, x3) -> c17(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3), EQ(s(x1), to(empty)))
   REACH(s(0), s(0), x2, x3) -> c17(IF1(true, isEmpty(x2), eq(s(0), from(x2)), eq(s(0), to(x2)), s(0), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c28_1, c29_2, c14_2, c16_2, c17_2


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

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

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c28_1, c29_2, c14_2, c16_2, c17_2


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

(225) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
We considered the (Usable) Rules:none
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_6
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_5
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = x_4
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = x_3
   POL(REACH(x_1, x_2, x_3, x_4)) = x_2
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1)) = x_1
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = 0
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1] + x_1
   POL(rest(x_1)) = 0
   POL(s(x_1)) = [1]
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c28_1, c29_2, c14_2, c16_2, c17_2


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

(227) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
We considered the (Usable) Rules:
   isEmpty(edge(z0, z1, z2)) -> false
   isEmpty(empty) -> true
And the Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(EQ(x_1, x_2)) = 0
   POL(IF1(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = x_2 + x_6
   POL(IF2(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_1 + x_5
   POL(IF3(x_1, x_2, x_3, x_4, x_5, x_6)) = [1] + x_4
   POL(IF4(x_1, x_2, x_3, x_4, x_5)) = [1] + x_3
   POL(REACH(x_1, x_2, x_3, x_4)) = [1] + x_2
   POL(UNION(x_1, x_2)) = 0
   POL(c14(x_1)) = x_1
   POL(c14(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1)) = x_1
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c23(x_1)) = x_1
   POL(c24(x_1)) = x_1
   POL(c25(x_1)) = x_1
   POL(c27(x_1)) = x_1
   POL(c28(x_1)) = x_1
   POL(c29(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(edge(x_1, x_2, x_3)) = 0
   POL(empty) = 0
   POL(eq(x_1, x_2)) = 0
   POL(false) = [1]
   POL(from(x_1)) = [1]
   POL(isEmpty(x_1)) = [1]
   POL(rest(x_1)) = 0
   POL(s(x_1)) = x_1
   POL(to(x_1)) = 0
   POL(true) = 0
   POL(union(x_1, x_2)) = [1] + x_2

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

(228)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c28_1, c29_2, c14_2, c16_2, c17_2


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

(229) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3)) by 
   REACH(0, 0, empty, x2) -> c17(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c17(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))

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

(230)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, 0, empty, x2) -> c17(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
K tuples:
   REACH(x0, x1, empty, x3) -> c17(IF1(eq(x0, x1), true, eq(x0, from(empty)), eq(x1, to(empty)), x0, x1, empty, x3))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c28_1, c29_2, c14_2, c16_2, c17_2


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

(231) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   REACH(0, 0, empty, x2) -> c17(IF1(true, true, eq(0, from(empty)), eq(0, to(empty)), 0, 0, empty, x2))

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

(232)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c28_1, c29_2, c14_2, c16_2, c17_2


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

(233) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty)) by 
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))

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

(234)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c28_1, c29_2, c14_2, c16_2, c17_2


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

(235) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF4(false, x0, x1, empty, x3) -> c28(REACH(to(empty), x1, union(empty, x3), empty)) by 
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))

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

(236)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c28_1, c29_2, c14_2, c16_2, c17_2


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

(237) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c28(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty)) by 
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))

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

(238)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c29_2, c14_2, c16_2, c17_2, c28_1


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

(239) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(to(edge(z0, z1, z2)), x1, union(z2, x3), empty), UNION(rest(edge(z0, z1, z2)), x3)) by 
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))

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

(240)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c29_2, c14_2, c16_2, c17_2, c28_1


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

(241) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF4(false, x0, x1, empty, x3) -> c29(REACH(to(empty), x1, union(empty, x3), empty), UNION(rest(empty), x3)) by 
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))

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

(242)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c29_2, c14_2, c16_2, c17_2, c28_1


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

(243) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF4(false, x0, x1, edge(z0, z1, z2), x3) -> c29(REACH(z1, x1, union(rest(edge(z0, z1, z2)), x3), empty), UNION(rest(edge(z0, z1, z2)), x3)) by 
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))

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

(244)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0)))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c14_2, c16_2, c17_2, c28_1, c29_2


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

(245) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, s(z0))) by REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
----------------------------------------

(246)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0)))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c14_2, c16_2, c17_2, c28_1, c29_2


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

(247) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c14(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, s(z0))) by REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
----------------------------------------

(248)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c14_2, c16_2, c17_2, c28_1, c29_2


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

(249) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1)) by REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
----------------------------------------

(250)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c14_2, c16_2, c17_2, c28_1, c29_2


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

(251) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1)) by REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
----------------------------------------

(252)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
S tuples:
   EQ(s(z0), s(z1)) -> c3(EQ(z0, z1))
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   EQ_2, UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4

Compound Symbols:   c3_1, c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c14_2, c16_2, c17_2, c28_1, c29_2


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

(253) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace EQ(s(z0), s(z1)) -> c3(EQ(z0, z1)) by 
   EQ(s(s(y0)), s(s(y1))) -> c3(EQ(s(y0), s(y1)))

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

(254)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
   EQ(s(s(y0)), s(s(y1))) -> c3(EQ(s(y0), s(y1)))
S tuples:
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
   EQ(s(s(y0)), s(s(y1))) -> c3(EQ(s(y0), s(y1)))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4, EQ_2

Compound Symbols:   c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c14_2, c16_2, c17_2, c28_1, c29_2, c3_1


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

(255) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   REACH(s(0), s(0), x2, x3) -> c17(EQ(s(0), to(x2)))
   REACH(s(0), s(0), x2, x3) -> c14(EQ(s(0), s(0)))
   REACH(s(0), s(0), x2, x3) -> c16(EQ(s(0), from(x2)))

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

(256)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
   EQ(s(s(y0)), s(s(y1))) -> c3(EQ(s(y0), s(y1)))
S tuples:
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), s(s(z0))))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), s(0)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(0), from(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(0), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
   EQ(s(s(y0)), s(s(y1))) -> c3(EQ(s(y0), s(y1)))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4, EQ_2

Compound Symbols:   c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c14_2, c16_2, c17_2, c28_1, c29_2, c3_1


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

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

(258)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   eq(0, 0) -> true
   eq(0, s(z0)) -> false
   eq(s(z0), 0) -> false
   eq(s(z0), s(z1)) -> eq(z0, z1)
   isEmpty(empty) -> true
   isEmpty(edge(z0, z1, z2)) -> false
   from(edge(z0, z1, z2)) -> z0
   to(edge(z0, z1, z2)) -> z1
   rest(edge(z0, z1, z2)) -> z2
   rest(empty) -> empty
   union(empty, z0) -> z0
   union(edge(z0, z1, z2), z3) -> edge(z0, z1, union(z2, z3))
Tuples:
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(0, s(z0), empty, x2) -> c14(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c14(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), empty, x2) -> c15(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c15(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(0, s(z0), empty, x2) -> c16(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c16(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(0, s(z0), empty, x2) -> c17(IF1(false, true, eq(0, from(empty)), eq(s(z0), to(empty)), 0, s(z0), empty, x2))
   REACH(s(z0), 0, empty, x2) -> c17(IF1(false, true, eq(s(z0), from(empty)), eq(0, to(empty)), s(z0), 0, empty, x2))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
   EQ(s(s(y0)), s(s(y1))) -> c3(EQ(s(y0), s(y1)))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
S tuples:
   UNION(edge(z0, z1, z2), z3) -> c7(UNION(z2, z3))
   IF1(false, z0, z1, z2, z3, z4, z5, z6) -> c19(IF2(z0, z1, z2, z3, z4, z5, z6))
   IF2(false, z0, z1, z2, z3, z4, z5) -> c21(IF3(z0, z1, z2, z3, z4, z5))
   IF3(true, z0, z1, z2, z3, z4) -> c25(IF4(z0, z1, z2, z3, z4))
   IF3(false, z0, z1, z2, z3, z4) -> c22(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c23(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF3(false, z0, z1, z2, z3, z4) -> c24(REACH(z1, z2, rest(z3), edge(from(z3), to(z3), z4)))
   IF4(false, z0, z1, z2, z3) -> c27(REACH(z0, z1, rest(z2), z3))
   REACH(0, s(z0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(0, s(z0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(0, from(x2)), eq(s(z0), to(x2)), 0, s(z0), x2, x3))
   REACH(s(z0), 0, x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(z0), from(x2)), eq(0, to(x2)), s(z0), 0, x2, x3))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c14(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), x1))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c14(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), x1))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c14(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, x1))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, x1, edge(0, x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c14(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c14(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), s(z1)))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c14(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c14(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), s(s(z1))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c15(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c15(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c15(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c15(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c15(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c15(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c15(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5))
   REACH(s(0), s(s(z0)), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c15(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c15(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c16(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5), EQ(x0, from(edge(x2, s(z0), x4))))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(x0, from(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c16(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(x0, from(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(s(z0), from(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c16(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(s(z0), from(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c16(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x0, from(edge(z0, z1, z2))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, x1, edge(0, x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c16(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c16(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z0), from(edge(x2, x3, x4))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c16(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5))
   REACH(s(x0), 0, edge(z0, z1, z2), x2) -> c16(IF1(false, isEmpty(edge(z0, z1, z2)), eq(s(x0), from(edge(z0, z1, z2))), eq(0, to(edge(z0, z1, z2))), s(x0), 0, edge(z0, z1, z2), x2), EQ(s(x0), z0))
   REACH(s(x0), 0, x1, x2) -> c16(IF1(false, isEmpty(x1), eq(s(x0), from(x1)), eq(0, to(x1)), s(x0), 0, x1, x2))
   REACH(s(s(z0)), s(0), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c16(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z0)), from(x2)))
   REACH(x0, s(z0), edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), false, x0, s(z0), edge(x2, 0, x4), x5), EQ(s(z0), to(edge(x2, 0, x4))))
   REACH(x0, s(z0), edge(x2, s(z1), x4), x5) -> c17(IF1(eq(x0, s(z0)), isEmpty(edge(x2, s(z1), x4)), eq(x0, from(edge(x2, s(z1), x4))), eq(z0, z1), x0, s(z0), edge(x2, s(z1), x4), x5), EQ(s(z0), to(edge(x2, s(z1), x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), isEmpty(edge(z0, z1, z2)), eq(x0, z0), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, from(edge(z0, z1, z2))), eq(x1, z1), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, from(edge(x2, x3, x4))), eq(s(z0), x3), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), x3), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(x0, 0, edge(x2, 0, x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, 0, x4)), eq(x0, from(edge(x2, 0, x4))), true, x0, 0, edge(x2, 0, x4), x5))
   REACH(x0, 0, edge(x2, s(z0), x4), x5) -> c17(IF1(eq(x0, 0), isEmpty(edge(x2, s(z0), x4)), eq(x0, from(edge(x2, s(z0), x4))), false, x0, 0, edge(x2, s(z0), x4), x5))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), from(edge(x2, x3, x4))), eq(0, x3), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, x1, edge(0, x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(0, x3, x4)), true, eq(x1, to(edge(0, x3, x4))), 0, x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(0, x1, edge(s(z0), x3, x4), x5) -> c17(IF1(eq(0, x1), isEmpty(edge(s(z0), x3, x4)), false, eq(x1, to(edge(s(z0), x3, x4))), 0, x1, edge(s(z0), x3, x4), x5), EQ(x1, to(edge(s(z0), x3, x4))))
   REACH(s(z0), x1, edge(0, x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(0, x3, x4)), false, eq(x1, to(edge(0, x3, x4))), s(z0), x1, edge(0, x3, x4), x5), EQ(x1, to(edge(0, x3, x4))))
   REACH(s(z0), x1, edge(s(z1), x3, x4), x5) -> c17(IF1(eq(s(z0), x1), isEmpty(edge(s(z1), x3, x4)), eq(z0, z1), eq(x1, to(edge(s(z1), x3, x4))), s(z0), x1, edge(s(z1), x3, x4), x5), EQ(x1, to(edge(s(z1), x3, x4))))
   REACH(x0, x1, edge(z0, z1, z2), x5) -> c17(IF1(eq(x0, x1), false, eq(x0, z0), eq(x1, to(edge(z0, z1, z2))), x0, x1, edge(z0, z1, z2), x5), EQ(x1, to(edge(z0, z1, z2))))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(0, x2), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, isEmpty(edge(x2, x3, x4)), eq(s(z0), x2), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(z0), edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(0, from(edge(x2, x3, x4))), eq(s(z0), to(edge(x2, x3, x4))), 0, s(z0), edge(x2, x3, x4), x5), EQ(s(z0), to(edge(x2, x3, x4))))
   REACH(s(z0), s(z1), edge(x2, x3, x4), x5) -> c17(IF1(eq(z0, z1), false, eq(s(z0), from(edge(x2, x3, x4))), eq(s(z1), to(edge(x2, x3, x4))), s(z0), s(z1), edge(x2, x3, x4), x5), EQ(s(z1), to(edge(x2, x3, x4))))
   REACH(s(z0), 0, edge(x2, x3, x4), x5) -> c17(IF1(false, false, eq(s(z0), from(edge(x2, x3, x4))), eq(0, to(edge(x2, x3, x4))), s(z0), 0, edge(x2, x3, x4), x5))
   REACH(0, s(x0), edge(z0, z1, z2), x2) -> c17(IF1(false, isEmpty(edge(z0, z1, z2)), eq(0, from(edge(z0, z1, z2))), eq(s(x0), to(edge(z0, z1, z2))), 0, s(x0), edge(z0, z1, z2), x2), EQ(s(x0), z1))
   REACH(0, s(x0), x1, x2) -> c17(IF1(false, isEmpty(x1), eq(0, from(x1)), eq(s(x0), to(x1)), 0, s(x0), x1, x2))
   REACH(s(0), s(s(z0)), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3), EQ(s(s(z0)), to(x2)))
   REACH(s(s(z0)), s(s(z1)), x2, x3) -> c17(IF1(eq(z0, z1), isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(s(z1)), to(x2)), s(s(z0)), s(s(z1)), x2, x3), EQ(s(s(z1)), to(x2)))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c28(REACH(to(edge(x2, x3, empty)), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c28(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c28(REACH(z1, x1, union(z2, x5), empty))
   IF4(false, x0, x1, empty, z0) -> c28(REACH(to(empty), x1, z0, empty))
   IF4(false, x0, x1, edge(x2, x3, empty), z0) -> c29(REACH(to(edge(x2, x3, empty)), x1, z0, empty), UNION(rest(edge(x2, x3, empty)), z0))
   IF4(false, x0, x1, edge(x2, x3, edge(z0, z1, z2)), z3) -> c29(REACH(to(edge(x2, x3, edge(z0, z1, z2))), x1, edge(z0, z1, union(z2, z3)), empty), UNION(rest(edge(x2, x3, edge(z0, z1, z2))), z3))
   IF4(false, x0, x1, edge(z0, z1, z2), x5) -> c29(REACH(z1, x1, union(z2, x5), empty), UNION(rest(edge(z0, z1, z2)), x5))
   IF4(false, x0, x1, empty, z0) -> c29(REACH(to(empty), x1, z0, empty), UNION(rest(empty), z0))
   REACH(z0, s(z1), edge(z2, 0, z3), z4) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, 0, z3)), eq(z0, z2), false, z0, s(z1), edge(z2, 0, z3), z4), EQ(z0, s(z1)))
   REACH(z0, s(z1), edge(z2, s(z3), z4), z5) -> c14(IF1(eq(z0, s(z1)), isEmpty(edge(z2, s(z3), z4)), eq(z0, z2), eq(z1, z3), z0, s(z1), edge(z2, s(z3), z4), z5), EQ(z0, s(z1)))
   REACH(z0, z1, edge(z2, z3, z4), z5) -> c14(IF1(eq(z0, z1), false, eq(z0, z2), eq(z1, z3), z0, z1, edge(z2, z3, z4), z5), EQ(z0, z1))
   EQ(s(s(y0)), s(s(y1))) -> c3(EQ(s(y0), s(y1)))
   REACH(s(0), s(s(z0)), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c14(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
   REACH(s(0), s(s(z0)), x2, x3) -> c16(IF1(false, isEmpty(x2), eq(s(0), from(x2)), eq(s(s(z0)), to(x2)), s(0), s(s(z0)), x2, x3))
   REACH(s(s(z0)), s(0), x2, x3) -> c17(IF1(false, isEmpty(x2), eq(s(s(z0)), from(x2)), eq(s(0), to(x2)), s(s(z0)), s(0), x2, x3))
K tuples:
   REACH(s(x0), s(x1), x2, x3) -> c14(EQ(s(x0), s(x1)))
   REACH(s(z0), s(z1), empty, x2) -> c14(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2), EQ(s(z0), s(z1)))
   REACH(s(z0), s(z1), empty, x2) -> c15(IF1(eq(z0, z1), true, eq(s(z0), from(empty)), eq(s(z1), to(empty)), s(z0), s(z1), empty, x2))
   REACH(s(x0), s(x1), empty, x3) -> c16(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
   REACH(s(x0), s(x1), empty, x3) -> c17(IF1(eq(x0, x1), true, eq(s(x0), from(empty)), eq(s(x1), to(empty)), s(x0), s(x1), empty, x3))
Defined Rule Symbols:   eq_2, isEmpty_1, from_1, to_1, rest_1, union_2

Defined Pair Symbols:   UNION_2, IF1_8, IF2_7, IF3_6, IF4_5, REACH_4, EQ_2

Compound Symbols:   c7_1, c19_1, c21_1, c25_1, c22_1, c23_1, c24_1, c27_1, c14_1, c15_1, c16_1, c17_1, c14_2, c16_2, c17_2, c28_1, c29_2, c3_1