KILLED
proof of input_BwcczGZ9G6.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 458 ms]
(2) CpxRelTRS
(3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
(7) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(8) CpxWeightedTrs
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxTypedWeightedTrs
    (11) CompletionProof [UPPER BOUND(ID), 0 ms]
    (12) CpxTypedWeightedCompleteTrs
        (13) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (14) CpxTypedWeightedCompleteTrs
        (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 19 ms]
        (16) CpxRNTS
        (17) InliningProof [UPPER BOUND(ID), 5 ms]
        (18) CpxRNTS
        (19) SimplificationProof [BOTH BOUNDS(ID, ID), 41 ms]
        (20) CpxRNTS
    (21) CompletionProof [UPPER BOUND(ID), 0 ms]
    (22) CpxTypedWeightedCompleteTrs
        (23) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (24) CpxRNTS
(25) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(26) CdtProblem
    (27) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (28) CdtProblem
    (29) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CdtProblem
    (31) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) CdtProblem
    (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CdtProblem
    (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 22 ms]
    (120) CdtProblem
    (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 36 ms]
    (122) CdtProblem
    (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtRewritingProof [BOTH BOUNDS(ID, ID), 25 ms]
    (128) CdtProblem
    (129) CdtRewritingProof [BOTH BOUNDS(ID, ID), 45 ms]
    (130) CdtProblem
    (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem


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

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


The TRS R consists of the following rules:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges)
   getNodeFromEdge(S(0), E(x, y)) -> x
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs))
   getNodeFromEdge(0, E(x, y)) -> x
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12)
   via(u, v, Nil, edges) -> Nil
   notEmpty(Cons(x, xs)) -> True
   notEmpty(Nil) -> False
   member(x, Nil) -> False
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges)
   goal(u, v, edges) -> reach(u, v, edges)

The (relative) TRS S consists of the following rules:

   !EQ(S(x), S(y)) -> !EQ(x, y)
   !EQ(0, S(y)) -> False
   !EQ(S(x), 0) -> False
   !EQ(0, 0) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges))
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges)
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs'))
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges)
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs)
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges)
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil)
   member[Ite](True, x, xs) -> True
   eqEdge[Ite](False, e21, e22, e11, e12) -> False
   eqEdge[Ite](True, e21, e22, e11, e12) -> True

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

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


The TRS R consists of the following rules:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges)
   getNodeFromEdge(S(0), E(x, y)) -> x
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs))
   getNodeFromEdge(0, E(x, y)) -> x
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12)
   via(u, v, Nil, edges) -> Nil
   notEmpty(Cons(x, xs)) -> True
   notEmpty(Nil) -> False
   member(x, Nil) -> False
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges)
   goal(u, v, edges) -> reach(u, v, edges)

The (relative) TRS S consists of the following rules:

   !EQ(S(x), S(y)) -> !EQ(x, y)
   !EQ(0, S(y)) -> False
   !EQ(S(x), 0) -> False
   !EQ(0, 0) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges))
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges)
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs'))
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges)
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs)
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges)
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil)
   member[Ite](True, x, xs) -> True
   eqEdge[Ite](False, e21, e22, e11, e12) -> False
   eqEdge[Ite](True, e21, e22, e11, e12) -> True

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

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

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


The TRS R consists of the following rules:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges)
   getNodeFromEdge(S(0'), E(x, y)) -> x
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs))
   getNodeFromEdge(0', E(x, y)) -> x
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12)
   via(u, v, Nil, edges) -> Nil
   notEmpty(Cons(x, xs)) -> True
   notEmpty(Nil) -> False
   member(x, Nil) -> False
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges)
   goal(u, v, edges) -> reach(u, v, edges)

The (relative) TRS S consists of the following rules:

   !EQ(S(x), S(y)) -> !EQ(x, y)
   !EQ(0', S(y)) -> False
   !EQ(S(x), 0') -> False
   !EQ(0', 0') -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges))
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges)
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs'))
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges)
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs)
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges)
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil)
   member[Ite](True, x, xs) -> True
   eqEdge[Ite](False, e21, e22, e11, e12) -> False
   eqEdge[Ite](True, e21, e22, e11, e12) -> True

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

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

(6)
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:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges)
   getNodeFromEdge(S(0), E(x, y)) -> x
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs))
   getNodeFromEdge(0, E(x, y)) -> x
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12)
   via(u, v, Nil, edges) -> Nil
   notEmpty(Cons(x, xs)) -> True
   notEmpty(Nil) -> False
   member(x, Nil) -> False
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges)
   goal(u, v, edges) -> reach(u, v, edges)
   !EQ(S(x), S(y)) -> !EQ(x, y)
   !EQ(0, S(y)) -> False
   !EQ(S(x), 0) -> False
   !EQ(0, 0) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges))
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges)
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs'))
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges)
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs)
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges)
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil)
   member[Ite](True, x, xs) -> True
   eqEdge[Ite](False, e21, e22, e11, e12) -> False
   eqEdge[Ite](True, e21, e22, e11, e12) -> True

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

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

(8)
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:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y [1]
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges) [1]
   getNodeFromEdge(S(0), E(x, y)) -> x [1]
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs)) [1]
   getNodeFromEdge(0, E(x, y)) -> x [1]
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) [1]
   via(u, v, Nil, edges) -> Nil [1]
   notEmpty(Cons(x, xs)) -> True [1]
   notEmpty(Nil) -> False [1]
   member(x, Nil) -> False [1]
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges) [1]
   goal(u, v, edges) -> reach(u, v, edges) [1]
   !EQ(S(x), S(y)) -> !EQ(x, y) [0]
   !EQ(0, S(y)) -> False [0]
   !EQ(S(x), 0) -> False [0]
   !EQ(0, 0) -> True [0]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges)) [0]
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges) [0]
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs')) [0]
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges) [0]
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs) [0]
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges) [0]
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil) [0]
   member[Ite](True, x, xs) -> True [0]
   eqEdge[Ite](False, e21, e22, e11, e12) -> False [0]
   eqEdge[Ite](True, e21, e22, e11, e12) -> True [0]

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

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

(10)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y [1]
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges) [1]
   getNodeFromEdge(S(0), E(x, y)) -> x [1]
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs)) [1]
   getNodeFromEdge(0, E(x, y)) -> x [1]
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) [1]
   via(u, v, Nil, edges) -> Nil [1]
   notEmpty(Cons(x, xs)) -> True [1]
   notEmpty(Nil) -> False [1]
   member(x, Nil) -> False [1]
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges) [1]
   goal(u, v, edges) -> reach(u, v, edges) [1]
   !EQ(S(x), S(y)) -> !EQ(x, y) [0]
   !EQ(0, S(y)) -> False [0]
   !EQ(S(x), 0) -> False [0]
   !EQ(0, 0) -> True [0]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges)) [0]
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges) [0]
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs')) [0]
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges) [0]
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs) [0]
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges) [0]
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil) [0]
   member[Ite](True, x, xs) -> True [0]
   eqEdge[Ite](False, e21, e22, e11, e12) -> False [0]
   eqEdge[Ite](True, e21, e22, e11, e12) -> True [0]

The TRS has the following type information:
getNodeFromEdge :: S:0 -> E -> S:0
S :: S:0 -> S:0
E :: S:0 -> S:0 -> E
via :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: E -> Cons:Nil -> Cons:Nil
via[Ite] :: True:False -> S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil
!EQ :: S:0 -> S:0 -> True:False
0 :: S:0
member :: E -> Cons:Nil -> True:False
member[Ite] :: True:False -> E -> Cons:Nil -> True:False
eqEdge :: E -> E -> True:False
eqEdge[Ite] :: True:False -> S:0 -> S:0 -> S:0 -> S:0 -> True:False
and :: True:False -> True:False -> True:False
Nil :: Cons:Nil
notEmpty :: Cons:Nil -> True:False
True :: True:False
False :: True:False
reach :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil
reach[Ite] :: True:False -> S:0 -> S:0 -> Cons:Nil -> Cons:Nil
goal :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil
via[Let] :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil

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

(11) 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:

   getNodeFromEdge_2
   notEmpty_1
   goal_3

(c) The following functions are completely defined:

   member_2
   reach_3
   eqEdge_2
   via_4
   !EQ_2
   and_2
   via[Ite]_5
   via[Let]_5
   member[Ite]_3
   reach[Ite]_4
   eqEdge[Ite]_5

Due to the following rules being added:

   !EQ(v0, v1) -> null_!EQ [0]
   and(v0, v1) -> null_and [0]
   via[Ite](v0, v1, v2, v3, v4) -> Nil [0]
   via[Let](v0, v1, v2, v3, v4) -> Nil [0]
   member[Ite](v0, v1, v2) -> null_member[Ite] [0]
   reach[Ite](v0, v1, v2, v3) -> Nil [0]
   eqEdge[Ite](v0, v1, v2, v3, v4) -> null_eqEdge[Ite] [0]
   eqEdge(v0, v1) -> null_eqEdge [0]
   via(v0, v1, v2, v3) -> Nil [0]

And the following fresh constants:    null_!EQ, null_and, null_member[Ite], null_eqEdge[Ite], null_eqEdge, const

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

(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:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y [1]
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges) [1]
   getNodeFromEdge(S(0), E(x, y)) -> x [1]
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs)) [1]
   getNodeFromEdge(0, E(x, y)) -> x [1]
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) [1]
   via(u, v, Nil, edges) -> Nil [1]
   notEmpty(Cons(x, xs)) -> True [1]
   notEmpty(Nil) -> False [1]
   member(x, Nil) -> False [1]
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges) [1]
   goal(u, v, edges) -> reach(u, v, edges) [1]
   !EQ(S(x), S(y)) -> !EQ(x, y) [0]
   !EQ(0, S(y)) -> False [0]
   !EQ(S(x), 0) -> False [0]
   !EQ(0, 0) -> True [0]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges)) [0]
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges) [0]
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs')) [0]
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges) [0]
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs) [0]
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges) [0]
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil) [0]
   member[Ite](True, x, xs) -> True [0]
   eqEdge[Ite](False, e21, e22, e11, e12) -> False [0]
   eqEdge[Ite](True, e21, e22, e11, e12) -> True [0]
   !EQ(v0, v1) -> null_!EQ [0]
   and(v0, v1) -> null_and [0]
   via[Ite](v0, v1, v2, v3, v4) -> Nil [0]
   via[Let](v0, v1, v2, v3, v4) -> Nil [0]
   member[Ite](v0, v1, v2) -> null_member[Ite] [0]
   reach[Ite](v0, v1, v2, v3) -> Nil [0]
   eqEdge[Ite](v0, v1, v2, v3, v4) -> null_eqEdge[Ite] [0]
   eqEdge(v0, v1) -> null_eqEdge [0]
   via(v0, v1, v2, v3) -> Nil [0]

The TRS has the following type information:
getNodeFromEdge :: S:0 -> E -> S:0
S :: S:0 -> S:0
E :: S:0 -> S:0 -> E
via :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: E -> Cons:Nil -> Cons:Nil
via[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil
!EQ :: S:0 -> S:0 -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
0 :: S:0
member :: E -> Cons:Nil -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
member[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> E -> Cons:Nil -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
eqEdge :: E -> E -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
eqEdge[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> S:0 -> S:0 -> S:0 -> S:0 -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
and :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
Nil :: Cons:Nil
notEmpty :: Cons:Nil -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
True :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
False :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
reach :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil
reach[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> S:0 -> S:0 -> Cons:Nil -> Cons:Nil
goal :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil
via[Let] :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
null_!EQ :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
null_and :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
null_member[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
null_eqEdge[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
null_eqEdge :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
const :: E

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

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

(14)
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:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y [1]
   via(S(x''), v, Cons(E(S(y'), y), xs), edges) -> via[Ite](!EQ(x'', y'), S(x''), v, Cons(E(S(y'), y), xs), edges) [1]
   via(0, v, Cons(E(S(y''), y), xs), edges) -> via[Ite](False, 0, v, Cons(E(S(y''), y), xs), edges) [1]
   via(S(x1), v, Cons(E(0, y), xs), edges) -> via[Ite](False, S(x1), v, Cons(E(0, y), xs), edges) [1]
   via(0, v, Cons(E(0, y), xs), edges) -> via[Ite](True, 0, v, Cons(E(0, y), xs), edges) [1]
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](null_!EQ, u, v, Cons(E(x, y), xs), edges) [1]
   getNodeFromEdge(S(0), E(x, y)) -> x [1]
   member(E(e11', e12'), Cons(E(e21', e22'), xs)) -> member[Ite](eqEdge[Ite](and(!EQ(e11', e21'), !EQ(e12', e22')), e21', e22', e11', e12'), E(e11', e12'), Cons(E(e21', e22'), xs)) [2]
   member(x', Cons(x, xs)) -> member[Ite](null_eqEdge, x', Cons(x, xs)) [1]
   getNodeFromEdge(0, E(x, y)) -> x [1]
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) [1]
   via(u, v, Nil, edges) -> Nil [1]
   notEmpty(Cons(x, xs)) -> True [1]
   notEmpty(Nil) -> False [1]
   member(x, Nil) -> False [1]
   reach(u, v, Cons(x14, xs'')) -> reach[Ite](member[Ite](eqEdge(E(u, v), x14), E(u, v), Cons(x14, xs'')), u, v, Cons(x14, xs'')) [2]
   reach(u, v, Nil) -> reach[Ite](False, u, v, Nil) [2]
   goal(u, v, edges) -> reach(u, v, edges) [1]
   !EQ(S(x), S(y)) -> !EQ(x, y) [0]
   !EQ(0, S(y)) -> False [0]
   !EQ(S(x), 0) -> False [0]
   !EQ(0, 0) -> True [0]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach[Ite](member(E(y, v), edges), y, v, edges)) [1]
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges) [0]
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs')) [0]
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges) [0]
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs) [0]
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges) [0]
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil) [0]
   member[Ite](True, x, xs) -> True [0]
   eqEdge[Ite](False, e21, e22, e11, e12) -> False [0]
   eqEdge[Ite](True, e21, e22, e11, e12) -> True [0]
   !EQ(v0, v1) -> null_!EQ [0]
   and(v0, v1) -> null_and [0]
   via[Ite](v0, v1, v2, v3, v4) -> Nil [0]
   via[Let](v0, v1, v2, v3, v4) -> Nil [0]
   member[Ite](v0, v1, v2) -> null_member[Ite] [0]
   reach[Ite](v0, v1, v2, v3) -> Nil [0]
   eqEdge[Ite](v0, v1, v2, v3, v4) -> null_eqEdge[Ite] [0]
   eqEdge(v0, v1) -> null_eqEdge [0]
   via(v0, v1, v2, v3) -> Nil [0]

The TRS has the following type information:
getNodeFromEdge :: S:0 -> E -> S:0
S :: S:0 -> S:0
E :: S:0 -> S:0 -> E
via :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: E -> Cons:Nil -> Cons:Nil
via[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil
!EQ :: S:0 -> S:0 -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
0 :: S:0
member :: E -> Cons:Nil -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
member[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> E -> Cons:Nil -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
eqEdge :: E -> E -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
eqEdge[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> S:0 -> S:0 -> S:0 -> S:0 -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
and :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
Nil :: Cons:Nil
notEmpty :: Cons:Nil -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
True :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
False :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
reach :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil
reach[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge -> S:0 -> S:0 -> Cons:Nil -> Cons:Nil
goal :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil
via[Let] :: S:0 -> S:0 -> Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
null_!EQ :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
null_and :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
null_member[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
null_eqEdge[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
null_eqEdge :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_eqEdge
const :: E

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

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

   0 => 0
   Nil => 0
   True => 2
   False => 1
   null_!EQ => 0
   null_and => 0
   null_member[Ite] => 0
   null_eqEdge[Ite] => 0
   null_eqEdge => 0
   const => 0

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

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

   !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0
   !EQ(z, z') -{ 0 }-> 1 :|: z' = 1 + y, y >= 0, z = 0
   !EQ(z, z') -{ 0 }-> 1 :|: x >= 0, z = 1 + x, z' = 0
   !EQ(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   !EQ(z, z') -{ 0 }-> !EQ(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqEdge(z, z') -{ 1 }-> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) :|: e21 >= 0, z = 1 + e11 + e12, e11 >= 0, e22 >= 0, e12 >= 0, z' = 1 + e21 + e22
   eqEdge(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 2 :|: z = 2, e21 >= 0, z2 = e12, e11 >= 0, e22 >= 0, z'' = e22, z1 = e11, e12 >= 0, z' = e21
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 1 :|: e21 >= 0, z = 1, z2 = e12, e11 >= 0, e22 >= 0, z'' = e22, z1 = e11, e12 >= 0, z' = e21
   eqEdge[Ite](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
   getNodeFromEdge(z, z') -{ 1 }-> x :|: z' = 1 + x + y, z = 1 + 0, x >= 0, y >= 0
   getNodeFromEdge(z, z') -{ 1 }-> x :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0
   getNodeFromEdge(z, z') -{ 1 }-> y :|: z' = 1 + x + y, x' >= 0, x >= 0, y >= 0, z = 1 + (1 + x')
   goal(z, z', z'') -{ 1 }-> reach(u, v, edges) :|: v >= 0, z'' = edges, z = u, z' = v, edges >= 0, u >= 0
   member(z, z') -{ 2 }-> member[Ite](eqEdge[Ite](and(!EQ(e11', e21'), !EQ(e12', e22')), e21', e22', e11', e12'), 1 + e11' + e12', 1 + (1 + e21' + e22') + xs) :|: xs >= 0, z = 1 + e11' + e12', z' = 1 + (1 + e21' + e22') + xs, e11' >= 0, e12' >= 0, e21' >= 0, e22' >= 0
   member(z, z') -{ 1 }-> member[Ite](0, x', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, x >= 0, z = x'
   member(z, z') -{ 1 }-> 1 :|: x >= 0, z = x, z' = 0
   member[Ite](z, z', z'') -{ 0 }-> member(x', xs) :|: z' = x', xs >= 0, z = 1, x' >= 0, x >= 0, z'' = 1 + x + xs
   member[Ite](z, z', z'') -{ 0 }-> 2 :|: z = 2, xs >= 0, z' = x, x >= 0, z'' = xs
   member[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0
   notEmpty(z) -{ 1 }-> 1 :|: z = 0
   reach(z, z', z'') -{ 2 }-> reach[Ite](member[Ite](eqEdge(1 + u + v, x14), 1 + u + v, 1 + x14 + xs''), u, v, 1 + x14 + xs'') :|: v >= 0, xs'' >= 0, z = u, z' = v, z'' = 1 + x14 + xs'', x14 >= 0, u >= 0
   reach(z, z', z'') -{ 2 }-> reach[Ite](1, u, v, 0) :|: z'' = 0, v >= 0, z = u, z' = v, u >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> via(u, v, edges, edges) :|: z'' = v, v >= 0, z = 1, z' = u, edges >= 0, z1 = edges, u >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> 1 + (1 + u + v) + 0 :|: z = 2, z'' = v, v >= 0, z' = u, edges >= 0, z1 = edges, u >= 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](2, 0, v, 1 + (1 + 0 + y) + xs, edges) :|: z'' = 1 + (1 + 0 + y) + xs, xs >= 0, v >= 0, y >= 0, z' = v, edges >= 0, z1 = edges, z = 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](1, 0, v, 1 + (1 + (1 + y'') + y) + xs, edges) :|: xs >= 0, v >= 0, y >= 0, z' = v, z'' = 1 + (1 + (1 + y'') + y) + xs, edges >= 0, y'' >= 0, z1 = edges, z = 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](1, 1 + x1, v, 1 + (1 + 0 + y) + xs, edges) :|: z'' = 1 + (1 + 0 + y) + xs, xs >= 0, x1 >= 0, v >= 0, y >= 0, z' = v, edges >= 0, z = 1 + x1, z1 = edges
   via(z, z', z'', z1) -{ 1 }-> via[Ite](0, u, v, 1 + (1 + x + y) + xs, edges) :|: xs >= 0, v >= 0, x >= 0, y >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + (1 + x + y) + xs, u >= 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](!EQ(x'', y'), 1 + x'', v, 1 + (1 + (1 + y') + y) + xs, edges) :|: z = 1 + x'', xs >= 0, v >= 0, y >= 0, z' = v, edges >= 0, y' >= 0, z1 = edges, z'' = 1 + (1 + (1 + y') + y) + xs, x'' >= 0
   via(z, z', z'', z1) -{ 1 }-> 0 :|: z'' = 0, v >= 0, z = u, z' = v, edges >= 0, z1 = edges, u >= 0
   via(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0
   via[Ite](z, z', z'', z1, z2) -{ 1 }-> via[Let](u, v, 1 + (1 + x + y) + xs, edges, reach[Ite](member(1 + y + v, edges), y, v, edges)) :|: z = 2, z'' = v, xs >= 0, v >= 0, z' = u, x >= 0, y >= 0, edges >= 0, z1 = 1 + (1 + x + y) + xs, z2 = edges, u >= 0
   via[Ite](z, z', z'', z1, z2) -{ 0 }-> via(u, v, xs, edges) :|: z'' = v, xs >= 0, v >= 0, z1 = 1 + x + xs, z = 1, z' = u, x >= 0, edges >= 0, z2 = edges, u >= 0
   via[Ite](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
   via[Let](z, z', z'', z1, z2) -{ 0 }-> via(u, v, xs, edges) :|: xs >= 0, v >= 0, z2 = 0, x >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + x + xs, u >= 0
   via[Let](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
   via[Let](z, z', z'', z1, z2) -{ 0 }-> 1 + x + (1 + x' + xs') :|: xs >= 0, v >= 0, x >= 0, x' >= 0, xs' >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + x + xs, z2 = 1 + x' + xs', u >= 0


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

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

   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 2 :|: z = 2, e21 >= 0, z2 = e12, e11 >= 0, e22 >= 0, z'' = e22, z1 = e11, e12 >= 0, z' = e21
   eqEdge[Ite](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
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 1 :|: e21 >= 0, z = 1, z2 = e12, e11 >= 0, e22 >= 0, z'' = e22, z1 = e11, e12 >= 0, z' = e21

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

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

   !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0
   !EQ(z, z') -{ 0 }-> 1 :|: z' = 1 + y, y >= 0, z = 0
   !EQ(z, z') -{ 0 }-> 1 :|: x >= 0, z = 1 + x, z' = 0
   !EQ(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   !EQ(z, z') -{ 0 }-> !EQ(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqEdge(z, z') -{ 1 }-> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) :|: e21 >= 0, z = 1 + e11 + e12, e11 >= 0, e22 >= 0, e12 >= 0, z' = 1 + e21 + e22
   eqEdge(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 2 :|: z = 2, e21 >= 0, z2 = e12, e11 >= 0, e22 >= 0, z'' = e22, z1 = e11, e12 >= 0, z' = e21
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 1 :|: e21 >= 0, z = 1, z2 = e12, e11 >= 0, e22 >= 0, z'' = e22, z1 = e11, e12 >= 0, z' = e21
   eqEdge[Ite](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
   getNodeFromEdge(z, z') -{ 1 }-> x :|: z' = 1 + x + y, z = 1 + 0, x >= 0, y >= 0
   getNodeFromEdge(z, z') -{ 1 }-> x :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0
   getNodeFromEdge(z, z') -{ 1 }-> y :|: z' = 1 + x + y, x' >= 0, x >= 0, y >= 0, z = 1 + (1 + x')
   goal(z, z', z'') -{ 1 }-> reach(u, v, edges) :|: v >= 0, z'' = edges, z = u, z' = v, edges >= 0, u >= 0
   member(z, z') -{ 2 }-> member[Ite](eqEdge[Ite](and(!EQ(e11', e21'), !EQ(e12', e22')), e21', e22', e11', e12'), 1 + e11' + e12', 1 + (1 + e21' + e22') + xs) :|: xs >= 0, z = 1 + e11' + e12', z' = 1 + (1 + e21' + e22') + xs, e11' >= 0, e12' >= 0, e21' >= 0, e22' >= 0
   member(z, z') -{ 1 }-> member[Ite](0, x', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, x >= 0, z = x'
   member(z, z') -{ 1 }-> 1 :|: x >= 0, z = x, z' = 0
   member[Ite](z, z', z'') -{ 0 }-> member(x', xs) :|: z' = x', xs >= 0, z = 1, x' >= 0, x >= 0, z'' = 1 + x + xs
   member[Ite](z, z', z'') -{ 0 }-> 2 :|: z = 2, xs >= 0, z' = x, x >= 0, z'' = xs
   member[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0
   notEmpty(z) -{ 1 }-> 1 :|: z = 0
   reach(z, z', z'') -{ 2 }-> reach[Ite](member[Ite](eqEdge(1 + u + v, x14), 1 + u + v, 1 + x14 + xs''), u, v, 1 + x14 + xs'') :|: v >= 0, xs'' >= 0, z = u, z' = v, z'' = 1 + x14 + xs'', x14 >= 0, u >= 0
   reach(z, z', z'') -{ 2 }-> reach[Ite](1, u, v, 0) :|: z'' = 0, v >= 0, z = u, z' = v, u >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> via(u, v, edges, edges) :|: z'' = v, v >= 0, z = 1, z' = u, edges >= 0, z1 = edges, u >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> 1 + (1 + u + v) + 0 :|: z = 2, z'' = v, v >= 0, z' = u, edges >= 0, z1 = edges, u >= 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](2, 0, v, 1 + (1 + 0 + y) + xs, edges) :|: z'' = 1 + (1 + 0 + y) + xs, xs >= 0, v >= 0, y >= 0, z' = v, edges >= 0, z1 = edges, z = 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](1, 0, v, 1 + (1 + (1 + y'') + y) + xs, edges) :|: xs >= 0, v >= 0, y >= 0, z' = v, z'' = 1 + (1 + (1 + y'') + y) + xs, edges >= 0, y'' >= 0, z1 = edges, z = 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](1, 1 + x1, v, 1 + (1 + 0 + y) + xs, edges) :|: z'' = 1 + (1 + 0 + y) + xs, xs >= 0, x1 >= 0, v >= 0, y >= 0, z' = v, edges >= 0, z = 1 + x1, z1 = edges
   via(z, z', z'', z1) -{ 1 }-> via[Ite](0, u, v, 1 + (1 + x + y) + xs, edges) :|: xs >= 0, v >= 0, x >= 0, y >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + (1 + x + y) + xs, u >= 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](!EQ(x'', y'), 1 + x'', v, 1 + (1 + (1 + y') + y) + xs, edges) :|: z = 1 + x'', xs >= 0, v >= 0, y >= 0, z' = v, edges >= 0, y' >= 0, z1 = edges, z'' = 1 + (1 + (1 + y') + y) + xs, x'' >= 0
   via(z, z', z'', z1) -{ 1 }-> 0 :|: z'' = 0, v >= 0, z = u, z' = v, edges >= 0, z1 = edges, u >= 0
   via(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0
   via[Ite](z, z', z'', z1, z2) -{ 1 }-> via[Let](u, v, 1 + (1 + x + y) + xs, edges, reach[Ite](member(1 + y + v, edges), y, v, edges)) :|: z = 2, z'' = v, xs >= 0, v >= 0, z' = u, x >= 0, y >= 0, edges >= 0, z1 = 1 + (1 + x + y) + xs, z2 = edges, u >= 0
   via[Ite](z, z', z'', z1, z2) -{ 0 }-> via(u, v, xs, edges) :|: z'' = v, xs >= 0, v >= 0, z1 = 1 + x + xs, z = 1, z' = u, x >= 0, edges >= 0, z2 = edges, u >= 0
   via[Ite](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
   via[Let](z, z', z'', z1, z2) -{ 0 }-> via(u, v, xs, edges) :|: xs >= 0, v >= 0, z2 = 0, x >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + x + xs, u >= 0
   via[Let](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
   via[Let](z, z', z'', z1, z2) -{ 0 }-> 1 + x + (1 + x' + xs') :|: xs >= 0, v >= 0, x >= 0, x' >= 0, xs' >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + x + xs, z2 = 1 + x' + xs', u >= 0


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

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

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

   !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0
   !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0
   !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0
   !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqEdge(z, z') -{ 1 }-> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) :|: e21 >= 0, z = 1 + e11 + e12, e11 >= 0, e22 >= 0, e12 >= 0, z' = 1 + e21 + e22
   eqEdge(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 2 :|: z = 2, z' >= 0, z1 >= 0, z'' >= 0, z2 >= 0
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 1 :|: z' >= 0, z = 1, z1 >= 0, z'' >= 0, z2 >= 0
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0
   getNodeFromEdge(z, z') -{ 1 }-> x :|: z' = 1 + x + y, z = 1 + 0, x >= 0, y >= 0
   getNodeFromEdge(z, z') -{ 1 }-> x :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0
   getNodeFromEdge(z, z') -{ 1 }-> y :|: z' = 1 + x + y, z - 2 >= 0, x >= 0, y >= 0
   goal(z, z', z'') -{ 1 }-> reach(z, z', z'') :|: z' >= 0, z'' >= 0, z >= 0
   member(z, z') -{ 2 }-> member[Ite](eqEdge[Ite](and(!EQ(e11', e21'), !EQ(e12', e22')), e21', e22', e11', e12'), 1 + e11' + e12', 1 + (1 + e21' + e22') + xs) :|: xs >= 0, z = 1 + e11' + e12', z' = 1 + (1 + e21' + e22') + xs, e11' >= 0, e12' >= 0, e21' >= 0, e22' >= 0
   member(z, z') -{ 1 }-> member[Ite](0, z, 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0
   member(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 0
   member[Ite](z, z', z'') -{ 0 }-> member(z', xs) :|: xs >= 0, z = 1, z' >= 0, x >= 0, z'' = 1 + x + xs
   member[Ite](z, z', z'') -{ 0 }-> 2 :|: z = 2, z'' >= 0, z' >= 0
   member[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0
   notEmpty(z) -{ 1 }-> 1 :|: z = 0
   reach(z, z', z'') -{ 2 }-> reach[Ite](member[Ite](eqEdge(1 + z + z', x14), 1 + z + z', 1 + x14 + xs''), z, z', 1 + x14 + xs'') :|: z' >= 0, xs'' >= 0, z'' = 1 + x14 + xs'', x14 >= 0, z >= 0
   reach(z, z', z'') -{ 2 }-> reach[Ite](1, z, z', 0) :|: z'' = 0, z' >= 0, z >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> via(z', z'', z1, z1) :|: z'' >= 0, z = 1, z1 >= 0, z' >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> 1 + (1 + z' + z'') + 0 :|: z = 2, z'' >= 0, z1 >= 0, z' >= 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](2, 0, z', 1 + (1 + 0 + y) + xs, z1) :|: z'' = 1 + (1 + 0 + y) + xs, xs >= 0, z' >= 0, y >= 0, z1 >= 0, z = 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](1, 0, z', 1 + (1 + (1 + y'') + y) + xs, z1) :|: xs >= 0, z' >= 0, y >= 0, z'' = 1 + (1 + (1 + y'') + y) + xs, z1 >= 0, y'' >= 0, z = 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](1, 1 + (z - 1), z', 1 + (1 + 0 + y) + xs, z1) :|: z'' = 1 + (1 + 0 + y) + xs, xs >= 0, z - 1 >= 0, z' >= 0, y >= 0, z1 >= 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](0, z, z', 1 + (1 + x + y) + xs, z1) :|: xs >= 0, z' >= 0, x >= 0, y >= 0, z1 >= 0, z'' = 1 + (1 + x + y) + xs, z >= 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](!EQ(z - 1, y'), 1 + (z - 1), z', 1 + (1 + (1 + y') + y) + xs, z1) :|: xs >= 0, z' >= 0, y >= 0, z1 >= 0, y' >= 0, z'' = 1 + (1 + (1 + y') + y) + xs, z - 1 >= 0
   via(z, z', z'', z1) -{ 1 }-> 0 :|: z'' = 0, z' >= 0, z1 >= 0, z >= 0
   via(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0
   via[Ite](z, z', z'', z1, z2) -{ 1 }-> via[Let](z', z'', 1 + (1 + x + y) + xs, z2, reach[Ite](member(1 + y + z'', z2), y, z'', z2)) :|: z = 2, xs >= 0, z'' >= 0, x >= 0, y >= 0, z2 >= 0, z1 = 1 + (1 + x + y) + xs, z' >= 0
   via[Ite](z, z', z'', z1, z2) -{ 0 }-> via(z', z'', xs, z2) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, z = 1, x >= 0, z2 >= 0, z' >= 0
   via[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0
   via[Let](z, z', z'', z1, z2) -{ 0 }-> via(z, z', xs, z1) :|: xs >= 0, z' >= 0, z2 = 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z >= 0
   via[Let](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0
   via[Let](z, z', z'', z1, z2) -{ 0 }-> 1 + x + (1 + x' + xs') :|: xs >= 0, z' >= 0, x >= 0, x' >= 0, xs' >= 0, z1 >= 0, z'' = 1 + x + xs, z2 = 1 + x' + xs', z >= 0


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

(21) 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:

   !EQ(v0, v1) -> null_!EQ [0]
   and(v0, v1) -> null_and [0]
   via[Ite](v0, v1, v2, v3, v4) -> null_via[Ite] [0]
   via[Let](v0, v1, v2, v3, v4) -> null_via[Let] [0]
   member[Ite](v0, v1, v2) -> null_member[Ite] [0]
   reach[Ite](v0, v1, v2, v3) -> null_reach[Ite] [0]
   eqEdge[Ite](v0, v1, v2, v3, v4) -> null_eqEdge[Ite] [0]
   getNodeFromEdge(v0, v1) -> null_getNodeFromEdge [0]
   via(v0, v1, v2, v3) -> null_via [0]
   member(v0, v1) -> null_member [0]
   eqEdge(v0, v1) -> null_eqEdge [0]
   notEmpty(v0) -> null_notEmpty [0]

And the following fresh constants:    null_!EQ, null_and, null_via[Ite], null_via[Let], null_member[Ite], null_reach[Ite], null_eqEdge[Ite], null_getNodeFromEdge, null_via, null_member, null_eqEdge, null_notEmpty, const

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

(22)
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:

   getNodeFromEdge(S(S(x')), E(x, y)) -> y [1]
   via(u, v, Cons(E(x, y), xs), edges) -> via[Ite](!EQ(u, x), u, v, Cons(E(x, y), xs), edges) [1]
   getNodeFromEdge(S(0), E(x, y)) -> x [1]
   member(x', Cons(x, xs)) -> member[Ite](eqEdge(x', x), x', Cons(x, xs)) [1]
   getNodeFromEdge(0, E(x, y)) -> x [1]
   eqEdge(E(e11, e12), E(e21, e22)) -> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) [1]
   via(u, v, Nil, edges) -> Nil [1]
   notEmpty(Cons(x, xs)) -> True [1]
   notEmpty(Nil) -> False [1]
   member(x, Nil) -> False [1]
   reach(u, v, edges) -> reach[Ite](member(E(u, v), edges), u, v, edges) [1]
   goal(u, v, edges) -> reach(u, v, edges) [1]
   !EQ(S(x), S(y)) -> !EQ(x, y) [0]
   !EQ(0, S(y)) -> False [0]
   !EQ(S(x), 0) -> False [0]
   !EQ(0, 0) -> True [0]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   via[Ite](True, u, v, Cons(E(x, y), xs), edges) -> via[Let](u, v, Cons(E(x, y), xs), edges, reach(y, v, edges)) [0]
   via[Let](u, v, Cons(x, xs), edges, Nil) -> via(u, v, xs, edges) [0]
   via[Let](u, v, Cons(x, xs), edges, Cons(x', xs')) -> Cons(x, Cons(x', xs')) [0]
   via[Ite](False, u, v, Cons(x, xs), edges) -> via(u, v, xs, edges) [0]
   member[Ite](False, x', Cons(x, xs)) -> member(x', xs) [0]
   reach[Ite](False, u, v, edges) -> via(u, v, edges, edges) [0]
   reach[Ite](True, u, v, edges) -> Cons(E(u, v), Nil) [0]
   member[Ite](True, x, xs) -> True [0]
   eqEdge[Ite](False, e21, e22, e11, e12) -> False [0]
   eqEdge[Ite](True, e21, e22, e11, e12) -> True [0]
   !EQ(v0, v1) -> null_!EQ [0]
   and(v0, v1) -> null_and [0]
   via[Ite](v0, v1, v2, v3, v4) -> null_via[Ite] [0]
   via[Let](v0, v1, v2, v3, v4) -> null_via[Let] [0]
   member[Ite](v0, v1, v2) -> null_member[Ite] [0]
   reach[Ite](v0, v1, v2, v3) -> null_reach[Ite] [0]
   eqEdge[Ite](v0, v1, v2, v3, v4) -> null_eqEdge[Ite] [0]
   getNodeFromEdge(v0, v1) -> null_getNodeFromEdge [0]
   via(v0, v1, v2, v3) -> null_via [0]
   member(v0, v1) -> null_member [0]
   eqEdge(v0, v1) -> null_eqEdge [0]
   notEmpty(v0) -> null_notEmpty [0]

The TRS has the following type information:
getNodeFromEdge :: S:0:null_getNodeFromEdge -> E -> S:0:null_getNodeFromEdge
S :: S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge
E :: S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> E
via :: S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
Cons :: E -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
via[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty -> S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
!EQ :: S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
0 :: S:0:null_getNodeFromEdge
member :: E -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
member[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty -> E -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
eqEdge :: E -> E -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
eqEdge[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty -> S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
and :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
Nil :: Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
notEmpty :: Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
True :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
False :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
reach :: S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
reach[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty -> S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
goal :: S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
via[Let] :: S:0:null_getNodeFromEdge -> S:0:null_getNodeFromEdge -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via -> Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
null_!EQ :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
null_and :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
null_via[Ite] :: Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
null_via[Let] :: Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
null_member[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
null_reach[Ite] :: Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
null_eqEdge[Ite] :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
null_getNodeFromEdge :: S:0:null_getNodeFromEdge
null_via :: Cons:Nil:null_via[Ite]:null_via[Let]:null_reach[Ite]:null_via
null_member :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
null_eqEdge :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
null_notEmpty :: True:False:null_!EQ:null_and:null_member[Ite]:null_eqEdge[Ite]:null_member:null_eqEdge:null_notEmpty
const :: E

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

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

   0 => 0
   Nil => 0
   True => 2
   False => 1
   null_!EQ => 0
   null_and => 0
   null_via[Ite] => 0
   null_via[Let] => 0
   null_member[Ite] => 0
   null_reach[Ite] => 0
   null_eqEdge[Ite] => 0
   null_getNodeFromEdge => 0
   null_via => 0
   null_member => 0
   null_eqEdge => 0
   null_notEmpty => 0
   const => 0

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

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

   !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0
   !EQ(z, z') -{ 0 }-> 1 :|: z' = 1 + y, y >= 0, z = 0
   !EQ(z, z') -{ 0 }-> 1 :|: x >= 0, z = 1 + x, z' = 0
   !EQ(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   !EQ(z, z') -{ 0 }-> !EQ(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqEdge(z, z') -{ 1 }-> eqEdge[Ite](and(!EQ(e11, e21), !EQ(e12, e22)), e21, e22, e11, e12) :|: e21 >= 0, z = 1 + e11 + e12, e11 >= 0, e22 >= 0, e12 >= 0, z' = 1 + e21 + e22
   eqEdge(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 2 :|: z = 2, e21 >= 0, z2 = e12, e11 >= 0, e22 >= 0, z'' = e22, z1 = e11, e12 >= 0, z' = e21
   eqEdge[Ite](z, z', z'', z1, z2) -{ 0 }-> 1 :|: e21 >= 0, z = 1, z2 = e12, e11 >= 0, e22 >= 0, z'' = e22, z1 = e11, e12 >= 0, z' = e21
   eqEdge[Ite](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
   getNodeFromEdge(z, z') -{ 1 }-> x :|: z' = 1 + x + y, z = 1 + 0, x >= 0, y >= 0
   getNodeFromEdge(z, z') -{ 1 }-> x :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0
   getNodeFromEdge(z, z') -{ 1 }-> y :|: z' = 1 + x + y, x' >= 0, x >= 0, y >= 0, z = 1 + (1 + x')
   getNodeFromEdge(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   goal(z, z', z'') -{ 1 }-> reach(u, v, edges) :|: v >= 0, z'' = edges, z = u, z' = v, edges >= 0, u >= 0
   member(z, z') -{ 1 }-> member[Ite](eqEdge(x', x), x', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, x >= 0, z = x'
   member(z, z') -{ 1 }-> 1 :|: x >= 0, z = x, z' = 0
   member(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   member[Ite](z, z', z'') -{ 0 }-> member(x', xs) :|: z' = x', xs >= 0, z = 1, x' >= 0, x >= 0, z'' = 1 + x + xs
   member[Ite](z, z', z'') -{ 0 }-> 2 :|: z = 2, xs >= 0, z' = x, x >= 0, z'' = xs
   member[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0
   notEmpty(z) -{ 1 }-> 1 :|: z = 0
   notEmpty(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   reach(z, z', z'') -{ 1 }-> reach[Ite](member(1 + u + v, edges), u, v, edges) :|: v >= 0, z'' = edges, z = u, z' = v, edges >= 0, u >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> via(u, v, edges, edges) :|: z'' = v, v >= 0, z = 1, z' = u, edges >= 0, z1 = edges, u >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0
   reach[Ite](z, z', z'', z1) -{ 0 }-> 1 + (1 + u + v) + 0 :|: z = 2, z'' = v, v >= 0, z' = u, edges >= 0, z1 = edges, u >= 0
   via(z, z', z'', z1) -{ 1 }-> via[Ite](!EQ(u, x), u, v, 1 + (1 + x + y) + xs, edges) :|: xs >= 0, v >= 0, x >= 0, y >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + (1 + x + y) + xs, u >= 0
   via(z, z', z'', z1) -{ 1 }-> 0 :|: z'' = 0, v >= 0, z = u, z' = v, edges >= 0, z1 = edges, u >= 0
   via(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0
   via[Ite](z, z', z'', z1, z2) -{ 0 }-> via[Let](u, v, 1 + (1 + x + y) + xs, edges, reach(y, v, edges)) :|: z = 2, z'' = v, xs >= 0, v >= 0, z' = u, x >= 0, y >= 0, edges >= 0, z1 = 1 + (1 + x + y) + xs, z2 = edges, u >= 0
   via[Ite](z, z', z'', z1, z2) -{ 0 }-> via(u, v, xs, edges) :|: z'' = v, xs >= 0, v >= 0, z1 = 1 + x + xs, z = 1, z' = u, x >= 0, edges >= 0, z2 = edges, u >= 0
   via[Ite](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
   via[Let](z, z', z'', z1, z2) -{ 0 }-> via(u, v, xs, edges) :|: xs >= 0, v >= 0, z2 = 0, x >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + x + xs, u >= 0
   via[Let](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
   via[Let](z, z', z'', z1, z2) -{ 0 }-> 1 + x + (1 + x' + xs') :|: xs >= 0, v >= 0, x >= 0, x' >= 0, xs' >= 0, z = u, z' = v, edges >= 0, z1 = edges, z'' = 1 + x + xs, z2 = 1 + x' + xs', u >= 0

Only complete derivations are relevant for the runtime complexity.

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

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

(26)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   getNodeFromEdge(S(S(z0)), E(z1, z2)) -> z2
   getNodeFromEdge(S(0), E(z0, z1)) -> z0
   getNodeFromEdge(0, E(z0, z1)) -> z0
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   notEmpty(Cons(z0, z1)) -> True
   notEmpty(Nil) -> False
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   goal(z0, z1, z2) -> reach(z0, z1, z2)
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   !EQ'(0, S(z0)) -> c1
   !EQ'(S(z0), 0) -> c2
   !EQ'(0, 0) -> c3
   AND(False, False) -> c4
   AND(True, False) -> c5
   AND(False, True) -> c6
   AND(True, True) -> c7
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), z5) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5)), REACH(z3, z1, z5))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> c11
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   MEMBER[ITE](True, z0, z1) -> c13
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   REACH[ITE](True, z0, z1, z2) -> c15
   EQEDGE[ITE](False, z0, z1, z2, z3) -> c16
   EQEDGE[ITE](True, z0, z1, z2, z3) -> c17
   GETNODEFROMEDGE(S(S(z0)), E(z1, z2)) -> c18
   GETNODEFROMEDGE(S(0), E(z0, z1)) -> c19
   GETNODEFROMEDGE(0, E(z0, z1)) -> c20
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(EQEDGE[ITE](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), AND(!EQ(z0, z2), !EQ(z1, z3)), !EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(EQEDGE[ITE](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), AND(!EQ(z0, z2), !EQ(z1, z3)), !EQ'(z1, z3))
   NOTEMPTY(Cons(z0, z1)) -> c27
   NOTEMPTY(Nil) -> c28
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   GOAL(z0, z1, z2) -> c30(REACH(z0, z1, z2))
S tuples:
   GETNODEFROMEDGE(S(S(z0)), E(z1, z2)) -> c18
   GETNODEFROMEDGE(S(0), E(z0, z1)) -> c19
   GETNODEFROMEDGE(0, E(z0, z1)) -> c20
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(EQEDGE[ITE](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), AND(!EQ(z0, z2), !EQ(z1, z3)), !EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(EQEDGE[ITE](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), AND(!EQ(z0, z2), !EQ(z1, z3)), !EQ'(z1, z3))
   NOTEMPTY(Cons(z0, z1)) -> c27
   NOTEMPTY(Nil) -> c28
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   GOAL(z0, z1, z2) -> c30(REACH(z0, z1, z2))
K tuples:none
Defined Rule Symbols:   getNodeFromEdge_2, via_4, member_2, eqEdge_2, notEmpty_1, reach_3, goal_3, !EQ_2, and_2, via[Ite]_5, via[Let]_5, member[Ite]_3, reach[Ite]_4, eqEdge[Ite]_5

Defined Pair Symbols:   !EQ'_2, AND_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, EQEDGE[ITE]_5, GETNODEFROMEDGE_2, VIA_4, MEMBER_2, EQEDGE_2, NOTEMPTY_1, REACH_3, GOAL_3

Compound Symbols:   c_1, c1, c2, c3, c4, c5, c6, c7, c8_2, c9_1, c10_1, c11, c12_1, c13, c14_1, c15, c16, c17, c18, c19, c20, c21_2, c22, c23_2, c24, c25_3, c26_3, c27, c28, c29_2, c30_1


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

(27) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   GOAL(z0, z1, z2) -> c30(REACH(z0, z1, z2))
Removed 17 trailing nodes:
   VIA[LET](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> c11
   !EQ'(0, S(z0)) -> c1
   AND(True, True) -> c7
   REACH[ITE](True, z0, z1, z2) -> c15
   AND(True, False) -> c5
   !EQ'(S(z0), 0) -> c2
   EQEDGE[ITE](False, z0, z1, z2, z3) -> c16
   GETNODEFROMEDGE(S(S(z0)), E(z1, z2)) -> c18
   EQEDGE[ITE](True, z0, z1, z2, z3) -> c17
   AND(False, False) -> c4
   GETNODEFROMEDGE(S(0), E(z0, z1)) -> c19
   !EQ'(0, 0) -> c3
   GETNODEFROMEDGE(0, E(z0, z1)) -> c20
   NOTEMPTY(Cons(z0, z1)) -> c27
   NOTEMPTY(Nil) -> c28
   MEMBER[ITE](True, z0, z1) -> c13
   AND(False, True) -> c6

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

(28)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   getNodeFromEdge(S(S(z0)), E(z1, z2)) -> z2
   getNodeFromEdge(S(0), E(z0, z1)) -> z0
   getNodeFromEdge(0, E(z0, z1)) -> z0
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   notEmpty(Cons(z0, z1)) -> True
   notEmpty(Nil) -> False
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   goal(z0, z1, z2) -> reach(z0, z1, z2)
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), z5) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5)), REACH(z3, z1, z5))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(EQEDGE[ITE](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), AND(!EQ(z0, z2), !EQ(z1, z3)), !EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(EQEDGE[ITE](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), AND(!EQ(z0, z2), !EQ(z1, z3)), !EQ'(z1, z3))
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
S tuples:
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(EQEDGE[ITE](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), AND(!EQ(z0, z2), !EQ(z1, z3)), !EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(EQEDGE[ITE](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), AND(!EQ(z0, z2), !EQ(z1, z3)), !EQ'(z1, z3))
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
K tuples:none
Defined Rule Symbols:   getNodeFromEdge_2, via_4, member_2, eqEdge_2, notEmpty_1, reach_3, goal_3, !EQ_2, and_2, via[Ite]_5, via[Let]_5, member[Ite]_3, reach[Ite]_4, eqEdge[Ite]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3

Compound Symbols:   c_1, c8_2, c9_1, c10_1, c12_1, c14_1, c21_2, c22, c23_2, c24, c25_3, c26_3, c29_2


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

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

(30)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   getNodeFromEdge(S(S(z0)), E(z1, z2)) -> z2
   getNodeFromEdge(S(0), E(z0, z1)) -> z0
   getNodeFromEdge(0, E(z0, z1)) -> z0
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   notEmpty(Cons(z0, z1)) -> True
   notEmpty(Nil) -> False
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   goal(z0, z1, z2) -> reach(z0, z1, z2)
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), z5) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5)), REACH(z3, z1, z5))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
S tuples:
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
K tuples:none
Defined Rule Symbols:   getNodeFromEdge_2, via_4, member_2, eqEdge_2, notEmpty_1, reach_3, goal_3, !EQ_2, and_2, via[Ite]_5, via[Let]_5, member[Ite]_3, reach[Ite]_4, eqEdge[Ite]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, REACH_3, EQEDGE_2

Compound Symbols:   c_1, c8_2, c9_1, c10_1, c12_1, c14_1, c21_2, c22, c23_2, c24, c29_2, c25_1, c26_1


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

(31) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   getNodeFromEdge(S(S(z0)), E(z1, z2)) -> z2
   getNodeFromEdge(S(0), E(z0, z1)) -> z0
   getNodeFromEdge(0, E(z0, z1)) -> z0
   notEmpty(Cons(z0, z1)) -> True
   notEmpty(Nil) -> False
   goal(z0, z1, z2) -> reach(z0, z1, z2)

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

(32)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), z5) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5)), REACH(z3, z1, z5))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
S tuples:
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, REACH_3, EQEDGE_2

Compound Symbols:   c_1, c8_2, c9_1, c10_1, c12_1, c14_1, c21_2, c22, c23_2, c24, c29_2, c25_1, c26_1


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

(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), z5) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5)), REACH(z3, z1, z5)) by 
   VIA[ITE](True, x0, z1, Cons(E(x2, z0), x4), z2) -> c8(VIA[LET](x0, z1, Cons(E(x2, z0), x4), z2, reach[Ite](member(E(z0, z1), z2), z0, z1, z2)), REACH(z0, z1, z2))

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

(34)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA[ITE](True, x0, z1, Cons(E(x2, z0), x4), z2) -> c8(VIA[LET](x0, z1, Cons(E(x2, z0), x4), z2, reach[Ite](member(E(z0, z1), z2), z0, z1, z2)), REACH(z0, z1, z2))
S tuples:
   VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, REACH_3, EQEDGE_2

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c21_2, c22, c23_2, c24, c29_2, c25_1, c26_1, c8_2


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

(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace VIA(z0, z1, Cons(E(z2, z3), z4), z5) -> c21(VIA[ITE](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5), !EQ'(z0, z2)) by 
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5), !EQ'(0, S(z0)))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5), !EQ'(S(z0), 0))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5), !EQ'(0, 0))

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA[ITE](True, x0, z1, Cons(E(x2, z0), x4), z2) -> c8(VIA[LET](x0, z1, Cons(E(x2, z0), x4), z2, reach[Ite](member(E(z0, z1), z2), z0, z1, z2)), REACH(z0, z1, z2))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5), !EQ'(0, S(z0)))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5), !EQ'(S(z0), 0))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5), !EQ'(0, 0))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5), !EQ'(0, S(z0)))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5), !EQ'(S(z0), 0))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5), !EQ'(0, 0))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, REACH_3, EQEDGE_2

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c22, c23_2, c24, c29_2, c25_1, c26_1, c8_2, c21_2


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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA[ITE](True, x0, z1, Cons(E(x2, z0), x4), z2) -> c8(VIA[LET](x0, z1, Cons(E(x2, z0), x4), z2, reach[Ite](member(E(z0, z1), z2), z0, z1, z2)), REACH(z0, z1, z2))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1))
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, REACH_3, EQEDGE_2

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c22, c23_2, c24, c29_2, c25_1, c26_1, c8_2, c21_2, c21_1


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

(39) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MEMBER(z0, Cons(z1, z2)) -> c23(MEMBER[ITE](eqEdge(z0, z1), z0, Cons(z1, z2)), EQEDGE(z0, z1)) by 
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA[ITE](True, x0, z1, Cons(E(x2, z0), x4), z2) -> c8(VIA[LET](x0, z1, Cons(E(x2, z0), x4), z2, reach[Ite](member(E(z0, z1), z2), z0, z1, z2)), REACH(z0, z1, z2))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, REACH_3, EQEDGE_2

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c22, c24, c29_2, c25_1, c26_1, c8_2, c21_2, c21_1, c23_2


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

(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(z0, z1, z2) -> c29(REACH[ITE](member(E(z0, z1), z2), z0, z1, z2), MEMBER(E(z0, z1), z2)) by 
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA[ITE](True, x0, z1, Cons(E(x2, z0), x4), z2) -> c8(VIA[LET](x0, z1, Cons(E(x2, z0), x4), z2, reach[Ite](member(E(z0, z1), z2), z0, z1, z2)), REACH(z0, z1, z2))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c22, c24, c25_1, c26_1, c8_2, c21_2, c21_1, c23_2, c29_2, c29_1


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

(43) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace VIA[ITE](True, x0, z1, Cons(E(x2, z0), x4), z2) -> c8(VIA[LET](x0, z1, Cons(E(x2, z0), x4), z2, reach[Ite](member(E(z0, z1), z2), z0, z1, z2)), REACH(z0, z1, z2)) by 
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Nil) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, reach[Ite](False, x3, x1, Nil)), REACH(x3, x1, Nil))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Nil) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, reach[Ite](False, x3, x1, Nil)), REACH(x3, x1, Nil))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1)))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c22, c24, c25_1, c26_1, c21_2, c21_1, c23_2, c29_2, c29_1, c8_2, c8_1


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

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace VIA(S(z0), x1, Cons(E(S(z1), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(z0), x1, Cons(E(S(z1), x3), x4), x5), !EQ'(S(z0), S(z1))) by 
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Nil) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, reach[Ite](False, x3, x1, Nil)), REACH(x3, x1, Nil))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3)))
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c22, c24, c25_1, c26_1, c21_1, c23_2, c29_2, c29_1, c8_2, c8_1, c21_2


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MEMBER(E(z0, z1), Cons(E(z2, z3), x2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x2)), EQEDGE(E(z0, z1), E(z2, z3))) by 
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Nil) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, reach[Ite](False, x3, x1, Nil)), REACH(x3, x1, Nil))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2)))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c22, c24, c25_1, c26_1, c21_1, c29_2, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace REACH(x0, x1, Cons(z1, z2)) -> c29(REACH[ITE](member[Ite](eqEdge(E(x0, x1), z1), E(x0, x1), Cons(z1, z2)), x0, x1, Cons(z1, z2)), MEMBER(E(x0, x1), Cons(z1, z2))) by 
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Nil) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, reach[Ite](False, x3, x1, Nil)), REACH(x3, x1, Nil))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3

Compound Symbols:   c_1, c9_1, c10_1, c12_1, c14_1, c22, c24, c25_1, c26_1, c21_1, c29_2, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1


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

(51) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA[ITE](False, z0, z1, Cons(z2, z3), z4) -> c9(VIA(z0, z1, z3, z4)) by 
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Nil) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, reach[Ite](False, x3, x1, Nil)), REACH(x3, x1, Nil))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3, VIA[ITE]_5

Compound Symbols:   c_1, c10_1, c12_1, c14_1, c22, c24, c25_1, c26_1, c21_1, c29_2, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c9_1


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

(53) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Nil) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, reach[Ite](False, x3, x1, Nil)), REACH(x3, x1, Nil)) by VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, via(z3, z1, Nil, Nil)), REACH(z3, z1, Nil))
----------------------------------------

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, via(z3, z1, Nil, Nil)), REACH(z3, z1, Nil))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3, VIA[ITE]_5

Compound Symbols:   c_1, c10_1, c12_1, c14_1, c22, c24, c25_1, c26_1, c21_1, c29_2, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c9_1


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

(55) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA[LET](z0, z1, Cons(z2, z3), z4, Nil) -> c10(VIA(z0, z1, z3, z4)) by 
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, via(z3, z1, Nil, Nil)), REACH(z3, z1, Nil))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, MEMBER[ITE]_3, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3, VIA[ITE]_5, VIA[LET]_5

Compound Symbols:   c_1, c12_1, c14_1, c22, c24, c25_1, c26_1, c21_1, c29_2, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c9_1, c10_1


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

(57) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace MEMBER[ITE](False, z0, Cons(z1, z2)) -> c12(MEMBER(z0, z2)) by 
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, via(z3, z1, Nil, Nil)), REACH(z3, z1, Nil))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, REACH[ITE]_4, VIA_4, MEMBER_2, EQEDGE_2, REACH_3, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3

Compound Symbols:   c_1, c14_1, c22, c24, c25_1, c26_1, c21_1, c29_2, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c9_1, c10_1, c12_1


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

(59) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace REACH[ITE](False, z0, z1, z2) -> c14(VIA(z0, z1, z2, z2)) by 
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, via(z3, z1, Nil, Nil)), REACH(z3, z1, Nil))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, Nil) -> c29(REACH[ITE](False, x0, x1, Nil), MEMBER(E(x0, x1), Nil))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA_4, MEMBER_2, EQEDGE_2, REACH_3, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4

Compound Symbols:   c_1, c22, c24, c25_1, c26_1, c21_1, c29_2, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c9_1, c10_1, c12_1, c14_1


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, via(z3, z1, Nil, Nil)), REACH(z3, z1, Nil))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
S tuples:
   VIA(z0, z1, Nil, z2) -> c22
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, VIA_4, MEMBER_2, EQEDGE_2, REACH_3, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4

Compound Symbols:   c_1, c22, c24, c25_1, c26_1, c21_1, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1


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

(63) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA(z0, z1, Nil, z2) -> c22 by 
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, via(z3, z1, Nil, Nil)), REACH(z3, z1, Nil))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
S tuples:
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, MEMBER_2, EQEDGE_2, VIA_4, REACH_3, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4

Compound Symbols:   c_1, c24, c25_1, c26_1, c21_1, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22


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

(65) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, via(z3, z1, Nil, Nil)), REACH(z3, z1, Nil)) by VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
----------------------------------------

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1))
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
S tuples:
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   !EQ'_2, MEMBER_2, EQEDGE_2, VIA_4, REACH_3, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4

Compound Symbols:   c_1, c24, c25_1, c26_1, c21_1, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22


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

(67) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) by 
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
S tuples:
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5), !EQ'(S(0), S(S(z0))))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(S(z0)), S(0)))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5), !EQ'(S(0), S(0)))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   MEMBER_2, EQEDGE_2, VIA_4, REACH_3, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c24, c25_1, c26_1, c21_1, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c_1


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

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
S tuples:
   MEMBER(z0, Nil) -> c24
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   MEMBER_2, EQEDGE_2, VIA_4, REACH_3, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c24, c25_1, c26_1, c21_1, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c_1


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

(71) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace MEMBER(z0, Nil) -> c24 by 
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2)))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
S tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   EQEDGE_2, VIA_4, REACH_3, VIA[ITE]_5, MEMBER_2, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c25_1, c26_1, c21_1, c29_1, c8_2, c8_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c_1, c24


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

(73) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2)) -> c8(VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(z1, z2), reach[Ite](member[Ite](eqEdge(E(x3, x1), z1), E(x3, x1), Cons(z1, z2)), x3, x1, Cons(z1, z2))), REACH(x3, x1, Cons(z1, z2))) by 
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
S tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   EQEDGE_2, VIA_4, REACH_3, VIA[ITE]_5, MEMBER_2, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c25_1, c26_1, c21_1, c29_1, c8_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c8_2, c_1, c24


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

(75) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA[ITE](True, x0, x1, Cons(E(x2, x3), x4), x5) -> c8(REACH(x3, x1, x5)) by 
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6)))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
S tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   EQEDGE_2, VIA_4, REACH_3, MEMBER_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c25_1, c26_1, c21_1, c29_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c8_2, c_1, c24, c8_1


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

(77) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA[LET](x0, x1, Cons(E(x2, x3), x4), Cons(x5, x6), Nil) -> c10(VIA(x0, x1, x4, Cons(x5, x6))) by 
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
S tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Cons(x5, x6)) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   EQEDGE_2, VIA_4, REACH_3, MEMBER_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c25_1, c26_1, c21_1, c29_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c8_2, c_1, c24, c8_1


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

(79) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA(x0, x1, Nil, Cons(x5, x6)) -> c22 by 
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil))
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
S tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   EQEDGE_2, VIA_4, REACH_3, MEMBER_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c25_1, c26_1, c21_1, c29_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c8_2, c_1, c24, c8_1


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

(81) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA[ITE](True, z0, z1, Cons(E(z2, z3), z4), Nil) -> c8(VIA[LET](z0, z1, Cons(E(z2, z3), z4), Nil, Nil), REACH(z3, z1, Nil)) by 
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
S tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2))
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   EQEDGE_2, VIA_4, REACH_3, MEMBER_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c25_1, c26_1, c21_1, c29_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1


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

(83) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace EQEDGE(E(z0, z1), E(z2, z3)) -> c25(!EQ'(z0, z2)) by 
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
S tuples:
   EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3))
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   EQEDGE_2, VIA_4, REACH_3, MEMBER_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2

Compound Symbols:   c26_1, c21_1, c29_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c25_1


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

(85) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace EQEDGE(E(z0, z1), E(z2, z3)) -> c26(!EQ'(z1, z3)) by 
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
S tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, REACH_3, MEMBER_2, VIA[ITE]_5, VIA[LET]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, EQEDGE_2

Compound Symbols:   c21_1, c29_1, c21_2, c23_2, c23_1, c29_2, c9_1, c10_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c25_1, c26_1


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

(87) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace VIA[LET](x0, x1, Cons(E(x2, x3), x4), Nil, Nil) -> c10(VIA(x0, x1, x4, Nil)) by 
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
S tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, REACH_3, MEMBER_2, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c29_1, c21_2, c23_2, c23_1, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1


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

(89) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace REACH(x0, x1, x2) -> c29(MEMBER(E(x0, x1), x2)) by 
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
S tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2)))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c23_1, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1


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

(91) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace VIA(S(x0), x1, Cons(E(S(x2), x3), x4), x5) -> c21(!EQ'(S(x0), S(x2))) by 
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
S tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c23_1, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1


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

(93) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER(E(x0, x1), Cons(E(x2, x3), x4)) -> c23(EQEDGE(E(x0, x1), E(x2, x3))) by 
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
S tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1


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

(95) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace VIA[ITE](False, 0, x0, Cons(E(S(x1), x2), x3), x4) -> c9(VIA(0, x0, x3, x4)) by 
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
S tuples:
   VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5))
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1


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

(97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace VIA(0, x1, Cons(E(S(z0), x3), x4), x5) -> c21(VIA[ITE](False, 0, x1, Cons(E(S(z0), x3), x4), x5)) by 
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
S tuples:
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1


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

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace VIA[ITE](False, S(x0), x1, Cons(E(0, x2), x3), x4) -> c9(VIA(S(x0), x1, x3, x4)) by 
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
S tuples:
   VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5))
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1


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

(101) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace VIA(S(z0), x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](False, S(z0), x1, Cons(E(0, x3), x4), x5)) by 
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1


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

(103) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace VIA[ITE](False, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c9(VIA(S(S(x0)), x1, x4, x5)) by 
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1


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

(105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace VIA[ITE](False, S(0), x0, Cons(E(S(S(x1)), x2), x3), x4) -> c9(VIA(S(0), x0, x3, x4)) by 
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, VIA[ITE]_5, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c9_1, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1


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

(107) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace VIA[ITE](False, S(S(x0)), x1, Cons(E(S(0), x2), x3), x4) -> c9(VIA(S(S(x0)), x1, x3, x4)) by 
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, S(x3)), x4)) -> c12(MEMBER(E(x0, S(x1)), x4)) by 
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER(E(x0, S(z0)), Cons(E(x2, S(z1)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), !EQ(z0, z1)), x2, S(z1), x0, S(z0)), E(x0, S(z0)), Cons(E(x2, S(z1)), x4)), EQEDGE(E(x0, S(z0)), E(x2, S(z1)))) by 
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(113) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER[ITE](False, E(x0, 0), Cons(E(x1, S(x2)), x3)) -> c12(MEMBER(E(x0, 0), x3)) by 
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER(E(x0, 0), Cons(E(x2, S(z0)), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, S(z0), x0, 0), E(x0, 0), Cons(E(x2, S(z0)), x4)), EQEDGE(E(x0, 0), E(x2, S(z0)))) by 
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)), EQEDGE(E(0, 0), E(S(y2), S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)), EQEDGE(E(S(y1), 0), E(0, S(z2))))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)), EQEDGE(E(0, 0), E(0, S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)), EQEDGE(E(0, 0), E(S(y2), S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)), EQEDGE(E(S(y1), 0), E(0, S(z2))))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)), EQEDGE(E(0, 0), E(0, S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)), EQEDGE(E(0, 0), E(S(y2), S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)), EQEDGE(E(S(y1), 0), E(0, S(z2))))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)), EQEDGE(E(0, 0), E(0, S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(0, 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER[ITE](False, E(x0, S(x1)), Cons(E(x2, 0), x3)) -> c12(MEMBER(E(x0, S(x1)), x3)) by 
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0)))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(121) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER(E(x0, S(z0)), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), False), x2, 0, x0, S(z0)), E(x0, S(z0)), Cons(E(x2, 0), x4)), EQEDGE(E(x0, S(z0)), E(x2, 0))) by 
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)), EQEDGE(E(0, S(z1)), E(S(y2), 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)), EQEDGE(E(S(y1), S(z1)), E(0, 0)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)), EQEDGE(E(0, S(z1)), E(0, 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)), EQEDGE(E(0, S(z1)), E(S(y2), 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)), EQEDGE(E(S(y1), S(z1)), E(0, 0)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)), EQEDGE(E(0, S(z1)), E(0, 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)), EQEDGE(E(0, S(z1)), E(S(y2), 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)), EQEDGE(E(S(y1), S(z1)), E(0, 0)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)), EQEDGE(E(0, S(z1)), E(0, 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(0, S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing tuple parts
----------------------------------------

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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(125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER[ITE](False, E(x0, 0), Cons(E(x1, 0), x2)) -> c12(MEMBER(E(x0, 0), x2)) by 
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y1)), S(y2)), y3))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y1)), S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5)))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y0), S(y1)), y2))) -> c12(MEMBER(E(0, 0), Cons(E(S(y0), S(y1)), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y0)), y1))) -> c12(MEMBER(E(0, 0), Cons(E(0, S(y0)), y1)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Nil))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Nil)))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y1)), S(y2)), y3))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y1)), S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5)))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y0), S(y1)), y2))) -> c12(MEMBER(E(0, 0), Cons(E(S(y0), S(y1)), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y0)), y1))) -> c12(MEMBER(E(0, 0), Cons(E(0, S(y0)), y1)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Nil))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Nil)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(127) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), !EQ(z1, z3)), S(y3), S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(S(y3), S(z3)))) by MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
----------------------------------------

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y1)), S(y2)), y3))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y1)), S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5)))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y0), S(y1)), y2))) -> c12(MEMBER(E(0, 0), Cons(E(S(y0), S(y1)), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y0)), y1))) -> c12(MEMBER(E(0, 0), Cons(E(0, S(y0)), y1)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Nil))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Nil)))
   MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(129) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MEMBER(E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), !EQ(z1, z3)), S(y2), S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), S(z3)), z4)), EQEDGE(E(0, S(z1)), E(S(y2), S(z3)))) by MEMBER(E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(z0, z2)), S(z1), S(z2), 0, S(z0)), E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)), EQEDGE(E(0, S(z0)), E(S(z1), S(z2))))
----------------------------------------

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y1)), S(y2)), y3))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y1)), S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5)))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y0), S(y1)), y2))) -> c12(MEMBER(E(0, 0), Cons(E(S(y0), S(y1)), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y0)), y1))) -> c12(MEMBER(E(0, 0), Cons(E(0, S(y0)), y1)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Nil))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Nil)))
   MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
   MEMBER(E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(z0, z2)), S(z1), S(z2), 0, S(z0)), E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)), EQEDGE(E(0, S(z0)), E(S(z1), S(z2))))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0)))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
   MEMBER(E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(z0, z2)), S(z1), S(z2), 0, S(z0)), E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)), EQEDGE(E(0, S(z0)), E(S(z1), S(z2))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER(E(x0, 0), Cons(E(x2, 0), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(x0, x2), True), x2, 0, x0, 0), E(x0, 0), Cons(E(x2, 0), x4)), EQEDGE(E(x0, 0), E(x2, 0))) by 
   MEMBER(E(S(y1), 0), Cons(E(S(y3), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), True), S(y3), 0, S(y1), 0), E(S(y1), 0), Cons(E(S(y3), 0), z2)), EQEDGE(E(S(y1), 0), E(S(y3), 0)))
   MEMBER(E(0, 0), Cons(E(S(y2), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), True), S(y2), 0, 0, 0), E(0, 0), Cons(E(S(y2), 0), z2)), EQEDGE(E(0, 0), E(S(y2), 0)))
   MEMBER(E(S(y1), 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), True), 0, 0, S(y1), 0), E(S(y1), 0), Cons(E(0, 0), z2)), EQEDGE(E(S(y1), 0), E(0, 0)))
   MEMBER(E(0, 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), True), 0, 0, 0, 0), E(0, 0), Cons(E(0, 0), z2)), EQEDGE(E(0, 0), E(0, 0)))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), True), S(S(y2)), 0, S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Nil)), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Nil)), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Nil)), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))), EQEDGE(E(0, 0), E(z1, 0)))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y1)), S(y2)), y3))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y1)), S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5)))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y0), S(y1)), y2))) -> c12(MEMBER(E(0, 0), Cons(E(S(y0), S(y1)), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y0)), y1))) -> c12(MEMBER(E(0, 0), Cons(E(0, S(y0)), y1)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Nil))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Nil)))
   MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
   MEMBER(E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(z0, z2)), S(z1), S(z2), 0, S(z0)), E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)), EQEDGE(E(0, S(z0)), E(S(z1), S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), True), S(y3), 0, S(y1), 0), E(S(y1), 0), Cons(E(S(y3), 0), z2)), EQEDGE(E(S(y1), 0), E(S(y3), 0)))
   MEMBER(E(0, 0), Cons(E(S(y2), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), True), S(y2), 0, 0, 0), E(0, 0), Cons(E(S(y2), 0), z2)), EQEDGE(E(0, 0), E(S(y2), 0)))
   MEMBER(E(S(y1), 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), True), 0, 0, S(y1), 0), E(S(y1), 0), Cons(E(0, 0), z2)), EQEDGE(E(S(y1), 0), E(0, 0)))
   MEMBER(E(0, 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), True), 0, 0, 0, 0), E(0, 0), Cons(E(0, 0), z2)), EQEDGE(E(0, 0), E(0, 0)))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), True), S(S(y2)), 0, S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Nil)), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Nil)), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Nil)), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))), EQEDGE(E(0, 0), E(z1, 0)))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
   MEMBER(E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(z0, z2)), S(z1), S(z2), 0, S(z0)), E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)), EQEDGE(E(0, S(z0)), E(S(z1), S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), True), S(y3), 0, S(y1), 0), E(S(y1), 0), Cons(E(S(y3), 0), z2)), EQEDGE(E(S(y1), 0), E(S(y3), 0)))
   MEMBER(E(0, 0), Cons(E(S(y2), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), True), S(y2), 0, 0, 0), E(0, 0), Cons(E(S(y2), 0), z2)), EQEDGE(E(0, 0), E(S(y2), 0)))
   MEMBER(E(S(y1), 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), True), 0, 0, S(y1), 0), E(S(y1), 0), Cons(E(0, 0), z2)), EQEDGE(E(S(y1), 0), E(0, 0)))
   MEMBER(E(0, 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), True), 0, 0, 0, 0), E(0, 0), Cons(E(0, 0), z2)), EQEDGE(E(0, 0), E(0, 0)))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), True), S(S(y2)), 0, S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Nil)), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Nil)), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Nil)), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))), EQEDGE(E(0, 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))), EQEDGE(E(0, 0), E(z1, 0)))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1


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

(133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing tuple parts
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   reach(z0, z1, z2) -> reach[Ite](member(E(z0, z1), z2), z0, z1, z2)
   reach[Ite](False, z0, z1, z2) -> via(z0, z1, z2, z2)
   reach[Ite](True, z0, z1, z2) -> Cons(E(z0, z1), Nil)
   member(z0, Cons(z1, z2)) -> member[Ite](eqEdge(z0, z1), z0, Cons(z1, z2))
   member(z0, Nil) -> False
   member[Ite](False, z0, Cons(z1, z2)) -> member(z0, z2)
   member[Ite](True, z0, z1) -> True
   eqEdge(E(z0, z1), E(z2, z3)) -> eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1)
   eqEdge[Ite](False, z0, z1, z2, z3) -> False
   eqEdge[Ite](True, z0, z1, z2, z3) -> True
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   !EQ(S(z0), S(z1)) -> !EQ(z0, z1)
   !EQ(0, S(z0)) -> False
   !EQ(S(z0), 0) -> False
   !EQ(0, 0) -> True
   via(z0, z1, Cons(E(z2, z3), z4), z5) -> via[Ite](!EQ(z0, z2), z0, z1, Cons(E(z2, z3), z4), z5)
   via(z0, z1, Nil, z2) -> Nil
   via[Ite](True, z0, z1, Cons(E(z2, z3), z4), z5) -> via[Let](z0, z1, Cons(E(z2, z3), z4), z5, reach(z3, z1, z5))
   via[Ite](False, z0, z1, Cons(z2, z3), z4) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Nil) -> via(z0, z1, z3, z4)
   via[Let](z0, z1, Cons(z2, z3), z4, Cons(z5, z6)) -> Cons(z2, Cons(z5, z6))
Tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(S(x2), x3), x4)) -> c12(MEMBER(E(S(x0), x1), x4))
   MEMBER[ITE](False, E(0, x0), Cons(E(S(x1), x2), x3)) -> c12(MEMBER(E(0, x0), x3))
   MEMBER[ITE](False, E(S(x0), x1), Cons(E(0, x2), x3)) -> c12(MEMBER(E(S(x0), x1), x3))
   MEMBER[ITE](False, E(0, x0), Cons(E(0, x1), x2)) -> c12(MEMBER(E(0, x0), x2))
   REACH[ITE](False, x0, x1, Nil) -> c14(VIA(x0, x1, Nil, Nil))
   REACH[ITE](False, x0, x1, Cons(E(x2, x3), x4)) -> c14(VIA(x0, x1, Cons(E(x2, x3), x4), Cons(E(x2, x3), x4)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1)))
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Cons(z5, z6)) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6)) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x3, x1), z5), E(x3, x1), Cons(z5, z6)), x3, x1, Cons(z5, z6))), REACH(x3, x1, Cons(z5, z6)))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6)) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(z5, z6), reach[Ite](member[Ite](eqEdge(E(x1, x0), z5), E(x1, x0), Cons(z5, z6)), x1, x0, Cons(z5, z6))), REACH(x1, x0, Cons(z5, z6)))
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), x5) -> c8(REACH(x3, x1, x5))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), x3) -> c8(REACH(x1, x0, x3))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Cons(x3, x4), Nil) -> c10(VIA(0, x0, x2, Cons(x3, x4)))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Cons(x5, x6), Nil) -> c10(VIA(S(S(x0)), x1, x4, Cons(x5, x6)))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Cons(x3, x4), Nil) -> c10(VIA(S(0), x0, x2, Cons(x3, x4)))
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   VIA[ITE](True, 0, x0, Cons(E(0, x1), x2), Nil) -> c8(VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   VIA[ITE](True, S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil) -> c8(VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil), REACH(x3, x1, Nil))
   VIA[ITE](True, S(0), x0, Cons(E(S(0), x1), x2), Nil) -> c8(VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil), REACH(x1, x0, Nil))
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   VIA[LET](0, x0, Cons(E(0, x1), x2), Nil, Nil) -> c10(VIA(0, x0, x2, Nil))
   VIA[LET](S(S(x0)), x1, Cons(E(S(S(x2)), x3), x4), Nil, Nil) -> c10(VIA(S(S(x0)), x1, x4, Nil))
   VIA[LET](S(0), x0, Cons(E(S(0), x1), x2), Nil, Nil) -> c10(VIA(S(0), x0, x2, Nil))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y1), y2), y3)), z4) -> c9(VIA(0, z0, Cons(E(S(y1), y2), y3), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y1), y2)), z4) -> c9(VIA(0, z0, Cons(E(0, y1), y2), z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4) -> c9(VIA(0, z0, Nil, z4))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c9(VIA(0, z0, Nil, Nil))
   VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y1, y2)) -> c9(VIA(0, z0, Nil, Cons(y1, y2)))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y2), y3)), z4) -> c9(VIA(S(z0), z1, Cons(E(0, y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(z0), z1, Nil, z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(S(y0)), z1, Nil, z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4) -> c9(VIA(S(0), z1, Nil, z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c9(VIA(S(z0), z1, Nil, Nil))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z1, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(y0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z1, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(z0), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(y0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y1, y2)) -> c9(VIA(S(0), z1, Nil, Cons(y1, y2)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(S(y2)), y3), y4)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), z5) -> c9(VIA(S(S(z0)), z1, Nil, z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(S(0), y2), y3)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(0, y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z5) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z5))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(S(z2)), z3), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), z4) -> c9(VIA(S(0), z0, Nil, z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Nil) -> c9(VIA(S(0), z0, Nil, Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(S(y1)), y2), y3)), z4) -> c9(VIA(S(0), z0, Cons(E(S(S(y1)), y2), y3), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(S(0), y1), y2)), z4) -> c9(VIA(S(0), z0, Cons(E(S(0), y1), y2), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(0), z0, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y1), Cons(E(S(0), y2), y3))), z4) -> c9(VIA(S(0), z0, Cons(E(0, y1), Cons(E(S(0), y2), y3)), z4))
   VIA[ITE](False, S(0), z0, Cons(E(S(S(z1)), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(0), z0, Cons(E(0, y2), Nil), Cons(y3, y4)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(S(y2)), y3), y4), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), z4) -> c9(VIA(S(S(z0)), z1, Nil, z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Nil) -> c9(VIA(S(S(z0)), z1, Nil, Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(S(0), y2), y3)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(S(0), y2), y3), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Nil), Cons(y2, y3)) -> c9(VIA(S(S(z0)), z1, Nil, Cons(y2, y3)))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(0, y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(0, y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Nil) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Nil))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Cons(E(S(0), y3), y4))), z4) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Cons(E(S(0), y3), y4)), z4))
   VIA[ITE](False, S(S(z0)), z1, Cons(E(S(0), z2), Cons(E(0, y2), Nil)), Cons(y3, y4)) -> c9(VIA(S(S(z0)), z1, Cons(E(0, y2), Nil), Cons(y3, y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, S(y3)), y4))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, S(z3)), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, S(y2)), y3))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, 0), y3))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, 0), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(z0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(S(y0), S(z1)), Nil))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c12(MEMBER(E(0, S(z1)), Nil))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(S(y3))), y4))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(S(y3))), y4)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(S(y2), S(y3)), y4))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(S(y2), S(y3)), y4)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(0, S(z1)), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y2)), y3))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(0, S(y2)), y3)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(0, S(z1)), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y2)), S(y3)), y4))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(y3)), y4)))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, S(y5)), y6))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5)))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Cons(E(y4, 0), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Cons(E(0, y4), y5))))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(z0, S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(S(y0), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Nil))) -> c12(MEMBER(E(S(y0), S(z1)), Cons(E(y2, S(y3)), Nil)))
   MEMBER[ITE](False, E(0, S(z1)), Cons(E(z2, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(0, S(z1)), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), S(z1)), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6)))) -> c12(MEMBER(E(S(S(y0)), S(z1)), Cons(E(y2, S(y3)), Cons(E(S(S(y4)), y5), y6))))
   MEMBER[ITE](False, E(z0, S(S(y1))), Cons(E(z2, 0), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6)))) -> c12(MEMBER(E(z0, S(S(y1))), Cons(E(y2, S(y3)), Cons(E(y4, S(S(y5))), y6))))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, 0), y2))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y2), y3), y4)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y1), y2), y3))) -> c12(MEMBER(E(0, 0), Cons(E(S(y1), y2), y3)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, y2), y3)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, y1), y2))) -> c12(MEMBER(E(0, 0), Cons(E(0, y1), y2)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(z0, 0), Nil))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(S(y0), 0), Nil))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Nil)) -> c12(MEMBER(E(0, 0), Nil))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y2)), y3), y4))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), y3), y4)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(S(y1), S(y2)), y3))) -> c12(MEMBER(E(S(y0), 0), Cons(E(S(y1), S(y2)), y3)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(S(S(y1)), S(y2)), y3))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y1)), S(y2)), y3)))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, S(y4)), y5))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4)))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Cons(E(y3, 0), y4))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(S(y3), y4), y5))))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4)))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Cons(E(0, y3), y4))))
   MEMBER[ITE](False, E(z0, 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Nil))) -> c12(MEMBER(E(S(y0), 0), Cons(E(y1, S(y2)), Nil)))
   MEMBER[ITE](False, E(S(S(y0)), 0), Cons(E(z1, 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5)))) -> c12(MEMBER(E(S(S(y0)), 0), Cons(E(y1, S(y2)), Cons(E(S(S(y3)), y4), y5))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(S(y0), S(y1)), y2))) -> c12(MEMBER(E(0, 0), Cons(E(S(y0), S(y1)), y2)))
   MEMBER[ITE](False, E(S(y0), 0), Cons(E(z1, 0), Cons(E(0, S(y1)), y2))) -> c12(MEMBER(E(S(y0), 0), Cons(E(0, S(y1)), y2)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y0)), y1))) -> c12(MEMBER(E(0, 0), Cons(E(0, S(y0)), y1)))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(S(y2), y3), y4))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3)))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Cons(E(0, y2), y3))))
   MEMBER[ITE](False, E(0, 0), Cons(E(z1, 0), Cons(E(y0, S(y1)), Nil))) -> c12(MEMBER(E(0, 0), Cons(E(y0, S(y1)), Nil)))
   MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
   MEMBER(E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(z0, z2)), S(z1), S(z2), 0, S(z0)), E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)), EQEDGE(E(0, S(z0)), E(S(z1), S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), True), S(y3), 0, S(y1), 0), E(S(y1), 0), Cons(E(S(y3), 0), z2)), EQEDGE(E(S(y1), 0), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), True), S(S(y2)), 0, S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Nil)), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Nil)), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(S(y2), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), True), S(y2), 0, 0, 0), E(0, 0), Cons(E(S(y2), 0), z2)))
   MEMBER(E(S(y1), 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), True), 0, 0, S(y1), 0), E(S(y1), 0), Cons(E(0, 0), z2)))
   MEMBER(E(0, 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), True), 0, 0, 0, 0), E(0, 0), Cons(E(0, 0), z2)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Nil)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))))
S tuples:
   VIA(0, x1, Cons(E(0, x3), x4), x5) -> c21(VIA[ITE](True, 0, x1, Cons(E(0, x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5) -> c21(VIA[ITE](!EQ(z0, z1), S(S(z0)), x1, Cons(E(S(S(z1)), x3), x4), x5), !EQ'(S(S(z0)), S(S(z1))))
   MEMBER(E(S(z0), x1), Cons(E(S(z1), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), !EQ(x1, x3)), S(z1), x3, S(z0), x1), E(S(z0), x1), Cons(E(S(z1), x3), x4)), EQEDGE(E(S(z0), x1), E(S(z1), x3)))
   MEMBER(E(0, x1), Cons(E(S(z0), x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), S(z0), x3, 0, x1), E(0, x1), Cons(E(S(z0), x3), x4)), EQEDGE(E(0, x1), E(S(z0), x3)))
   MEMBER(E(S(z0), x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(x1, x3)), 0, x3, S(z0), x1), E(S(z0), x1), Cons(E(0, x3), x4)), EQEDGE(E(S(z0), x1), E(0, x3)))
   MEMBER(E(0, x1), Cons(E(0, x3), x4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(True, !EQ(x1, x3)), 0, x3, 0, x1), E(0, x1), Cons(E(0, x3), x4)), EQEDGE(E(0, x1), E(0, x3)))
   REACH(z0, z1, Cons(E(z2, z3), x3)) -> c29(REACH[ITE](member[Ite](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, z3, z0, z1), E(z0, z1), Cons(E(z2, z3), x3)), z0, z1, Cons(E(z2, z3), x3)), MEMBER(E(z0, z1), Cons(E(z2, z3), x3)))
   REACH(x0, x1, Nil) -> c1(REACH[ITE](False, x0, x1, Nil))
   REACH(x0, x1, Nil) -> c1(MEMBER(E(x0, x1), Nil))
   VIA(0, x0, Nil, x4) -> c22
   VIA(S(x0), x1, Nil, x4) -> c22
   VIA(S(S(x0)), x1, Nil, x5) -> c22
   VIA(S(0), x0, Nil, x4) -> c22
   VIA(x0, x1, Nil, Nil) -> c22
   VIA(S(0), x1, Cons(E(S(S(z0)), x3), x4), x5) -> c21(VIA[ITE](False, S(0), x1, Cons(E(S(S(z0)), x3), x4), x5))
   VIA(S(S(z0)), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](False, S(S(z0)), x1, Cons(E(S(0), x3), x4), x5))
   VIA(S(0), x1, Cons(E(S(0), x3), x4), x5) -> c21(VIA[ITE](True, S(0), x1, Cons(E(S(0), x3), x4), x5))
   MEMBER(E(x0, x1), Nil) -> c24
   MEMBER(E(x0, S(x1)), Nil) -> c24
   MEMBER(E(x0, 0), Nil) -> c24
   MEMBER(E(S(x0), x1), Nil) -> c24
   MEMBER(E(0, x0), Nil) -> c24
   VIA(0, x0, Nil, Cons(z2, z3)) -> c22
   VIA(S(x0), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(S(x0)), x1, Nil, Cons(z2, z3)) -> c22
   VIA(S(0), x0, Nil, Cons(z2, z3)) -> c22
   EQEDGE(E(S(S(y0)), z1), E(S(S(y1)), z3)) -> c25(!EQ'(S(S(y0)), S(S(y1))))
   EQEDGE(E(z0, S(S(y0))), E(z2, S(S(y1)))) -> c26(!EQ'(S(S(y0)), S(S(y1))))
   REACH(z0, S(y1), Cons(E(y2, S(y3)), y4)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, S(y3)), y4)))
   REACH(z0, 0, Cons(E(y1, S(y2)), y3)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, S(y2)), y3)))
   REACH(z0, S(y1), Cons(E(y2, 0), y3)) -> c29(MEMBER(E(z0, S(y1)), Cons(E(y2, 0), y3)))
   REACH(z0, 0, Cons(E(y1, 0), y2)) -> c29(MEMBER(E(z0, 0), Cons(E(y1, 0), y2)))
   REACH(S(y0), z1, Cons(E(S(y2), y3), y4)) -> c29(MEMBER(E(S(y0), z1), Cons(E(S(y2), y3), y4)))
   REACH(0, z1, Cons(E(S(y1), y2), y3)) -> c29(MEMBER(E(0, z1), Cons(E(S(y1), y2), y3)))
   REACH(S(y0), z1, Cons(E(0, y2), y3)) -> c29(MEMBER(E(S(y0), z1), Cons(E(0, y2), y3)))
   REACH(0, z1, Cons(E(0, y1), y2)) -> c29(MEMBER(E(0, z1), Cons(E(0, y1), y2)))
   REACH(z0, z1, Cons(E(y2, y3), y4)) -> c29(MEMBER(E(z0, z1), Cons(E(y2, y3), y4)))
   REACH(z0, z1, Nil) -> c29(MEMBER(E(z0, z1), Nil))
   REACH(z0, S(y1), Nil) -> c29(MEMBER(E(z0, S(y1)), Nil))
   REACH(z0, 0, Nil) -> c29(MEMBER(E(z0, 0), Nil))
   REACH(S(y0), z1, Nil) -> c29(MEMBER(E(S(y0), z1), Nil))
   REACH(0, z1, Nil) -> c29(MEMBER(E(0, z1), Nil))
   VIA(S(S(y0)), z1, Cons(E(S(S(y1)), z3), z4), z5) -> c21(!EQ'(S(S(y0)), S(S(y1))))
   MEMBER(E(S(S(y0)), z1), Cons(E(S(S(y2)), z3), z4)) -> c23(EQEDGE(E(S(S(y0)), z1), E(S(S(y2)), z3)))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(S(y3), y4), y5)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Cons(E(0, y3), y4)), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), z4) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), z4))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Nil) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Nil))
   VIA(0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, 0, z0, Cons(E(S(z1), z2), Nil), Cons(y3, y4)))
   VIA(S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Cons(E(0, y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(S(y3)), y4), y5)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(0), z1, Cons(E(0, z2), Nil), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Nil) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Nil))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(S(y2)), y3), y4)), z4))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Cons(E(S(0), y3), y4)), z4))
   VIA(S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Cons(E(S(0), y2), y3)), z4))
   VIA(S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(z0), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)) -> c21(VIA[ITE](False, S(S(y0)), z1, Cons(E(0, z2), Nil), Cons(y3, y4)))
   VIA(S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)) -> c21(VIA[ITE](False, S(0), z1, Cons(E(0, z2), Nil), Cons(y2, y3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), !EQ(z1, z3)), 0, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(S(y1), S(z1)), E(0, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(0, S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), !EQ(z1, z3)), 0, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(0, S(z3)), z4)), EQEDGE(E(0, S(z1)), E(0, S(z3))))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), !EQ(z1, z3)), S(S(y2)), S(z3), S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), S(z3)), z4)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), S(z3))))
   MEMBER(E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y1), S(y3))), z2, S(S(y3)), z0, S(S(y1))), E(z0, S(S(y1))), Cons(E(z2, S(S(y3))), z4)), EQEDGE(E(z0, S(S(y1))), E(z2, S(S(y3)))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, S(y6)), y7))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Cons(E(y5, 0), y6))), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y5), y6), y7))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(S(y4), y5), y6))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Cons(E(0, y4), y5))), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), z2, S(z3), z0, S(z1)), E(z0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(z0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), !EQ(z1, z3)), z2, S(z3), S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, S(z3))))
   MEMBER(E(0, S(z1)), Cons(E(z2, S(z3)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), !EQ(z1, z3)), z2, S(z3), 0, S(z1)), E(0, S(z1)), Cons(E(z2, S(z3)), Nil)), EQEDGE(E(0, S(z1)), E(z2, S(z3))))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), !EQ(z1, z3)), z2, S(z3), S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, S(z3)), Cons(E(S(S(y5)), y6), y7))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, S(z3))))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(S(y2), z3)), z2, S(z3), z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, S(z3)), Cons(E(y5, S(S(y6))), y7))), EQEDGE(E(z0, S(S(y2))), E(z2, S(z3))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), S(z2), S(y1), 0), E(S(y1), 0), Cons(E(S(y3), S(z2)), z3)), EQEDGE(E(S(y1), 0), E(S(y3), S(z2))))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), S(z2), S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), S(z2)), z3)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, S(y5)), y6))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Cons(E(y4, 0), y5))), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(z0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), False), z1, S(z2), z0, 0), E(z0, 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(z0, 0), E(z1, S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), False), z1, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(z1, S(z2)), Nil)), EQEDGE(E(S(y1), 0), E(z1, S(z2))))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), False), z1, S(z2), S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, S(z2)), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), 0), E(z1, S(z2))))
   MEMBER(E(0, 0), Cons(E(S(y2), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), S(z2), 0, 0), E(0, 0), Cons(E(S(y2), S(z2)), z3)))
   MEMBER(E(S(y1), 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, S(z2), S(y1), 0), E(S(y1), 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(0, S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, S(z2), 0, 0), E(0, 0), Cons(E(0, S(z2)), z3)))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Cons(E(0, y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, S(z2)), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), False), z1, S(z2), 0, 0), E(0, 0), Cons(E(z1, S(z2)), Nil)))
   MEMBER(E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), False), S(y3), 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(S(y3), 0), z3)), EQEDGE(E(S(y1), S(z1)), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), False), S(S(y2)), 0, S(S(y0)), S(z1)), E(S(S(y0)), S(z1)), Cons(E(S(S(y2)), 0), z3)), EQEDGE(E(S(S(y0)), S(z1)), E(S(S(y2)), 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, 0), y5))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), y5), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, y4), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Nil)), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), y5), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(S(y5))), y6))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(S(y4), S(y5)), y6))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(0, S(y4)), y5))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(S(S(y4)), S(y5)), y6))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(y7)), y8)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, 0), y7)))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(y6), y7), y8)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(0, y6), y7)))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(z1)), E(z0, S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(z0, S(z1)), E(z2, 0)))
   MEMBER(E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z2), False), z2, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Nil))), EQEDGE(E(S(y1), S(z1)), E(z2, 0)))
   MEMBER(E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z2), False), z2, 0, S(S(y1)), S(z1)), E(S(S(y1)), S(z1)), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(S(S(y6)), y7), y8)))), EQEDGE(E(S(S(y1)), S(z1)), E(z2, 0)))
   MEMBER(E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), False), z2, 0, z0, S(S(y2))), E(z0, S(S(y2))), Cons(E(z2, 0), Cons(E(y4, S(y5)), Cons(E(y6, S(S(y7))), y8)))), EQEDGE(E(z0, S(S(y2))), E(z2, 0)))
   MEMBER(E(0, S(z1)), Cons(E(S(y2), 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), False), S(y2), 0, 0, S(z1)), E(0, S(z1)), Cons(E(S(y2), 0), z3)))
   MEMBER(E(S(y1), S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), False), 0, 0, S(y1), S(z1)), E(S(y1), S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(0, 0), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), False), 0, 0, 0, S(z1)), E(0, S(z1)), Cons(E(0, 0), z3)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), y4), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, y3), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Nil)))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(S(y3), S(y4)), y5))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(0, S(y3)), y4))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))))
   MEMBER(E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z2), False), z2, 0, 0, S(z1)), E(0, S(z1)), Cons(E(z2, 0), Cons(E(y3, S(y4)), Nil))))
   MEMBER(E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z2), !EQ(z1, z3)), S(z2), S(z3), S(z0), S(z1)), E(S(z0), S(z1)), Cons(E(S(z2), S(z3)), z4)), EQEDGE(E(S(z0), S(z1)), E(S(z2), S(z3))))
   MEMBER(E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)) -> c23(MEMBER[ITE](eqEdge[Ite](and(False, !EQ(z0, z2)), S(z1), S(z2), 0, S(z0)), E(0, S(z0)), Cons(E(S(z1), S(z2)), z3)), EQEDGE(E(0, S(z0)), E(S(z1), S(z2))))
   MEMBER(E(S(y1), 0), Cons(E(S(y3), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), S(y3)), True), S(y3), 0, S(y1), 0), E(S(y1), 0), Cons(E(S(y3), 0), z2)), EQEDGE(E(S(y1), 0), E(S(y3), 0)))
   MEMBER(E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y0)), S(S(y2))), True), S(S(y2)), 0, S(S(y0)), 0), E(S(S(y0)), 0), Cons(E(S(S(y2)), 0), z2)), EQEDGE(E(S(S(y0)), 0), E(S(S(y2)), 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, 0), y4))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), y4), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, y3), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Nil)), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Nil)), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), y4), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(S(y3), S(y4)), y5))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(S(S(y3)), S(y4)), y5))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, S(y6)), y7)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(y5, 0), y6)))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(y5), y6), y7)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(0, y5), y6)))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(z0, z1), True), z1, 0, z0, 0), E(z0, 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(z0, 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Nil))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(S(y1)), z1), True), z1, 0, S(S(y1)), 0), E(S(S(y1)), 0), Cons(E(z1, 0), Cons(E(y3, S(y4)), Cons(E(S(S(y5)), y6), y7)))), EQEDGE(E(S(S(y1)), 0), E(z1, 0)))
   MEMBER(E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), z1), True), z1, 0, S(y1), 0), E(S(y1), 0), Cons(E(z1, 0), Cons(E(0, S(y3)), y4))), EQEDGE(E(S(y1), 0), E(z1, 0)))
   MEMBER(E(0, 0), Cons(E(S(y2), 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, S(y2)), True), S(y2), 0, 0, 0), E(0, 0), Cons(E(S(y2), 0), z2)))
   MEMBER(E(S(y1), 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(S(y1), 0), True), 0, 0, S(y1), 0), E(S(y1), 0), Cons(E(0, 0), z2)))
   MEMBER(E(0, 0), Cons(E(0, 0), z2)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, 0), True), 0, 0, 0, 0), E(0, 0), Cons(E(0, 0), z2)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), y3), y4))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, y2), y3))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Nil)) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Nil)))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(S(y2), S(y3)), y4))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(0, S(y2)), y3))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(S(y4), y5), y6)))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Cons(E(0, y4), y5)))))
   MEMBER(E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))) -> c23(MEMBER[ITE](eqEdge[Ite](and(!EQ(0, z1), True), z1, 0, 0, 0), E(0, 0), Cons(E(z1, 0), Cons(E(y2, S(y3)), Nil))))
K tuples:none
Defined Rule Symbols:   reach_3, reach[Ite]_4, member_2, member[Ite]_3, eqEdge_2, eqEdge[Ite]_5, and_2, !EQ_2, via_4, via[Ite]_5, via[Let]_5

Defined Pair Symbols:   VIA_4, MEMBER_2, REACH_3, MEMBER[ITE]_3, REACH[ITE]_4, !EQ'_2, VIA[ITE]_5, VIA[LET]_5, EQEDGE_2

Compound Symbols:   c21_1, c21_2, c23_2, c29_2, c12_1, c14_1, c1_1, c22, c_1, c24, c8_2, c8_1, c10_1, c25_1, c26_1, c29_1, c23_1, c9_1