/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


KILLED
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 290 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
(13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxTypedWeightedTrs
    (21) CompletionProof [UPPER BOUND(ID), 0 ms]
    (22) CpxTypedWeightedCompleteTrs
        (23) NarrowingProof [BOTH BOUNDS(ID, ID), 106 ms]
        (24) CpxTypedWeightedCompleteTrs
        (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms]
        (26) CpxRNTS
        (27) SimplificationProof [BOTH BOUNDS(ID, ID), 3 ms]
        (28) CpxRNTS
    (29) CompletionProof [UPPER BOUND(ID), 0 ms]
    (30) CpxTypedWeightedCompleteTrs
        (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms]
        (32) CpxRNTS
(33) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(34) CdtProblem
    (35) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 51 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms]
    (46) CdtProblem
    (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms]
    (52) CdtProblem
    (53) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 ms]
    (58) CdtProblem
    (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (62) CdtProblem
    (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 122 ms]
    (66) CdtProblem
    (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 259 ms]
    (70) CdtProblem
    (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 128 ms]
    (72) CdtProblem
    (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms]
    (74) CdtProblem
    (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 ms]
    (76) CdtProblem
    (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms]
    (78) CdtProblem
    (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms]
    (84) CdtProblem
    (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms]
    (86) CdtProblem
    (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 63 ms]
    (90) CdtProblem
    (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 60 ms]
    (94) CdtProblem
    (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms]
    (98) CdtProblem
    (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms]
    (102) CdtProblem
    (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms]
    (104) CdtProblem
    (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms]
    (106) CdtProblem
    (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms]
    (110) CdtProblem
    (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms]
    (114) CdtProblem
    (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 73 ms]
    (118) CdtProblem
    (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms]
    (122) CdtProblem
    (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms]
    (124) CdtProblem
    (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms]
    (126) CdtProblem
    (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms]
    (128) CdtProblem
    (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms]
    (130) CdtProblem
    (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms]
    (134) CdtProblem
    (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms]
    (138) CdtProblem
    (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 ms]
    (140) CdtProblem
    (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms]
    (142) CdtProblem
    (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms]
    (144) CdtProblem
    (145) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
    (148) CdtProblem


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

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, x)) -> false
   app(app(eq, app(s, x)), 0) -> false
   app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
   app(app(or, true), y) -> true
   app(app(or, false), y) -> y
   app(app(union, empty), h) -> h
   app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
   app(app(app(app(reach, x), y), empty), h) -> false
   app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
   app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
   app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)

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

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2


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

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


The TRS R consists of the following rules:

   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, x)) -> false
   app(app(eq, app(s, x)), 0) -> false
   app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
   app(app(or, true), y) -> true
   app(app(or, false), y) -> y
   app(app(union, empty), h) -> h
   app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
   app(app(app(app(reach, x), y), empty), h) -> false
   app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
   app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
   app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)

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

   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2

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

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

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


The TRS R consists of the following rules:

   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, x)) -> false
   app(app(eq, app(s, x)), 0) -> false
   app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
   app(app(or, true), y) -> true
   app(app(or, false), y) -> y
   app(app(union, empty), h) -> h
   app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
   app(app(app(app(reach, x), y), empty), h) -> false
   app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
   app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
   app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)

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

   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2

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

(5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(6)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, x)) -> false
   app(app(eq, app(s, x)), 0) -> false
   app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
   app(app(or, true), y) -> true
   app(app(or, false), y) -> y
   app(app(union, empty), h) -> h
   app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
   app(app(app(app(reach, x), y), empty), h) -> false
   app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
   app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
   app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)

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

   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2

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

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

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(app(eq, 0'), 0') -> true
   app(app(eq, 0'), app(s, x)) -> false
   app(app(eq, app(s, x)), 0') -> false
   app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
   app(app(or, true), y) -> true
   app(app(or, false), y) -> y
   app(app(union, empty), h) -> h
   app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
   app(app(app(app(reach, x), y), empty), h) -> false
   app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
   app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
   app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)

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

   encArg(eq) -> eq
   encArg(0') -> 0'
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_eq -> eq
   encode_0 -> 0'
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2

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

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

(10)
Obligation:
Innermost TRS:
Rules:
app(app(eq, 0'), 0') -> true
app(app(eq, 0'), app(s, x)) -> false
app(app(eq, app(s, x)), 0') -> false
app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
app(app(or, true), y) -> true
app(app(or, false), y) -> y
app(app(union, empty), h) -> h
app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
app(app(app(app(reach, x), y), empty), h) -> false
app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
app(app(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) -> nil
app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)
encArg(eq) -> eq
encArg(0') -> 0'
encArg(true) -> true
encArg(s) -> s
encArg(false) -> false
encArg(or) -> or
encArg(union) -> union
encArg(empty) -> empty
encArg(edge) -> edge
encArg(reach) -> reach
encArg(if_reach_1) -> if_reach_1
encArg(if_reach_2) -> if_reach_2
encArg(map) -> map
encArg(nil) -> nil
encArg(cons) -> cons
encArg(filter) -> filter
encArg(filter2) -> filter2
encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
encode_eq -> eq
encode_0 -> 0'
encode_true -> true
encode_s -> s
encode_false -> false
encode_or -> or
encode_union -> union
encode_empty -> empty
encode_edge -> edge
encode_reach -> reach
encode_if_reach_1 -> if_reach_1
encode_if_reach_2 -> if_reach_2
encode_map -> map
encode_nil -> nil
encode_cons -> cons
encode_filter -> filter
encode_filter2 -> filter2

Types:
app :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
eq :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
0' :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
true :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
s :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
false :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
or :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
union :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
empty :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
edge :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
reach :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
if_reach_1 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
if_reach_2 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
map :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
nil :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
cons :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
filter :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
filter2 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encArg :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
cons_app :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_app :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_eq :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_0 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_true :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_s :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_false :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_or :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_union :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_empty :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_edge :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_reach :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_if_reach_1 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_if_reach_2 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_map :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_nil :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_cons :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_filter :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_filter2 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
hole_eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app1_3 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
gen_eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app2_3 :: Nat -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app

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

(11) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
app, encArg

They will be analysed ascendingly in the following order:
app < encArg

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

(12)
Obligation:
Innermost TRS:
Rules:
app(app(eq, 0'), 0') -> true
app(app(eq, 0'), app(s, x)) -> false
app(app(eq, app(s, x)), 0') -> false
app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
app(app(or, true), y) -> true
app(app(or, false), y) -> y
app(app(union, empty), h) -> h
app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
app(app(app(app(reach, x), y), empty), h) -> false
app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
app(app(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) -> nil
app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)
encArg(eq) -> eq
encArg(0') -> 0'
encArg(true) -> true
encArg(s) -> s
encArg(false) -> false
encArg(or) -> or
encArg(union) -> union
encArg(empty) -> empty
encArg(edge) -> edge
encArg(reach) -> reach
encArg(if_reach_1) -> if_reach_1
encArg(if_reach_2) -> if_reach_2
encArg(map) -> map
encArg(nil) -> nil
encArg(cons) -> cons
encArg(filter) -> filter
encArg(filter2) -> filter2
encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
encode_eq -> eq
encode_0 -> 0'
encode_true -> true
encode_s -> s
encode_false -> false
encode_or -> or
encode_union -> union
encode_empty -> empty
encode_edge -> edge
encode_reach -> reach
encode_if_reach_1 -> if_reach_1
encode_if_reach_2 -> if_reach_2
encode_map -> map
encode_nil -> nil
encode_cons -> cons
encode_filter -> filter
encode_filter2 -> filter2

Types:
app :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
eq :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
0' :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
true :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
s :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
false :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
or :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
union :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
empty :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
edge :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
reach :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
if_reach_1 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
if_reach_2 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
map :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
nil :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
cons :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
filter :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
filter2 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encArg :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
cons_app :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_app :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_eq :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_0 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_true :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_s :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_false :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_or :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_union :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_empty :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_edge :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_reach :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_if_reach_1 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_if_reach_2 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_map :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_nil :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_cons :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_filter :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
encode_filter2 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
hole_eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app1_3 :: eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app
gen_eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app2_3 :: Nat -> eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app


Generator Equations:
gen_eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app2_3(0) <=> eq
gen_eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app2_3(+(x, 1)) <=> cons_app(eq, gen_eq:0':true:s:false:or:union:empty:edge:reach:if_reach_1:if_reach_2:map:nil:cons:filter:filter2:cons_app2_3(x))


The following defined symbols remain to be analysed:
app, encArg

They will be analysed ascendingly in the following order:
app < encArg

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

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

(14)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, x)) -> false
   app(app(eq, app(s, x)), 0) -> false
   app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
   app(app(or, true), y) -> true
   app(app(or, false), y) -> y
   app(app(union, empty), h) -> h
   app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
   app(app(app(app(reach, x), y), empty), h) -> false
   app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
   app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
   app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
   app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(app(filter, f), nil) -> nil
   app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2

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

(15) NonCtorToCtorProof (UPPER BOUND(ID))
transformed non-ctor to ctor-system
----------------------------------------

(16)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
   app(c_app(eq, c_app(s, x)), 0) -> false
   app(c_app(c_app(c_app(c_app(if_reach_2, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> true
   app(c_app(eq, 0), 0) -> true
   app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y)
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs)
   app(c_app(or, false), y) -> y
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
   app(c_app(map, f), nil) -> nil
   app(c_app(filter, f), nil) -> nil
   app(c_app(c_app(c_app(reach, x), y), empty), h) -> false
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
   app(c_app(or, true), y) -> true
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(c_app(union, empty), h) -> h
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
   app(c_app(eq, 0), c_app(s, x)) -> false

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

   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2))
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   app(x0, x1) -> c_app(x0, x1)

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

(17) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(18)
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:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(eq, c_app(s, x)), 0) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> true [1]
   app(c_app(eq, 0), 0) -> true [1]
   app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(or, false), y) -> y [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty)) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(c_app(reach, x), y), empty), h) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h) [1]
   app(c_app(or, true), y) -> true [1]
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1]
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h)) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(union, empty), h) -> h [1]
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h) [1]
   app(c_app(eq, 0), c_app(s, x)) -> false [1]
   encArg(eq) -> eq [0]
   encArg(0) -> 0 [0]
   encArg(true) -> true [0]
   encArg(s) -> s [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(union) -> union [0]
   encArg(empty) -> empty [0]
   encArg(edge) -> edge [0]
   encArg(reach) -> reach [0]
   encArg(if_reach_1) -> if_reach_1 [0]
   encArg(if_reach_2) -> if_reach_2 [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_eq -> eq [0]
   encode_0 -> 0 [0]
   encode_true -> true [0]
   encode_s -> s [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_union -> union [0]
   encode_empty -> empty [0]
   encode_edge -> edge [0]
   encode_reach -> reach [0]
   encode_if_reach_1 -> if_reach_1 [0]
   encode_if_reach_2 -> if_reach_2 [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   app(x0, x1) -> c_app(x0, x1) [0]

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

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

(20)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(eq, c_app(s, x)), 0) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> true [1]
   app(c_app(eq, 0), 0) -> true [1]
   app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(or, false), y) -> y [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty)) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(c_app(reach, x), y), empty), h) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h) [1]
   app(c_app(or, true), y) -> true [1]
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1]
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h)) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(union, empty), h) -> h [1]
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h) [1]
   app(c_app(eq, 0), c_app(s, x)) -> false [1]
   encArg(eq) -> eq [0]
   encArg(0) -> 0 [0]
   encArg(true) -> true [0]
   encArg(s) -> s [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(union) -> union [0]
   encArg(empty) -> empty [0]
   encArg(edge) -> edge [0]
   encArg(reach) -> reach [0]
   encArg(if_reach_1) -> if_reach_1 [0]
   encArg(if_reach_2) -> if_reach_2 [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_eq -> eq [0]
   encode_0 -> 0 [0]
   encode_true -> true [0]
   encode_s -> s [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_union -> union [0]
   encode_empty -> empty [0]
   encode_edge -> edge [0]
   encode_reach -> reach [0]
   encode_if_reach_1 -> if_reach_1 [0]
   encode_if_reach_2 -> if_reach_2 [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   app(x0, x1) -> c_app(x0, x1) [0]

The TRS has the following type information:
app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
c_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encArg :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
cons_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app
encode_filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app

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

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

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

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
none

(c) The following functions are completely defined:

   encArg_1
   encode_app_2
   encode_eq
   encode_0
   encode_true
   encode_s
   encode_false
   encode_or
   encode_union
   encode_empty
   encode_edge
   encode_reach
   encode_if_reach_1
   encode_if_reach_2
   encode_map
   encode_nil
   encode_cons
   encode_filter
   encode_filter2
   app_2

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_eq -> null_encode_eq [0]
   encode_0 -> null_encode_0 [0]
   encode_true -> null_encode_true [0]
   encode_s -> null_encode_s [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_union -> null_encode_union [0]
   encode_empty -> null_encode_empty [0]
   encode_edge -> null_encode_edge [0]
   encode_reach -> null_encode_reach [0]
   encode_if_reach_1 -> null_encode_if_reach_1 [0]
   encode_if_reach_2 -> null_encode_if_reach_2 [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_filter -> null_encode_filter [0]
   encode_filter2 -> null_encode_filter2 [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_eq, null_encode_0, null_encode_true, null_encode_s, null_encode_false, null_encode_or, null_encode_union, null_encode_empty, null_encode_edge, null_encode_reach, null_encode_if_reach_1, null_encode_if_reach_2, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_app

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

(22)
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:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(eq, c_app(s, x)), 0) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> true [1]
   app(c_app(eq, 0), 0) -> true [1]
   app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(or, false), y) -> y [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty)) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(c_app(reach, x), y), empty), h) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h) [1]
   app(c_app(or, true), y) -> true [1]
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1]
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h)) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(union, empty), h) -> h [1]
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h) [1]
   app(c_app(eq, 0), c_app(s, x)) -> false [1]
   encArg(eq) -> eq [0]
   encArg(0) -> 0 [0]
   encArg(true) -> true [0]
   encArg(s) -> s [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(union) -> union [0]
   encArg(empty) -> empty [0]
   encArg(edge) -> edge [0]
   encArg(reach) -> reach [0]
   encArg(if_reach_1) -> if_reach_1 [0]
   encArg(if_reach_2) -> if_reach_2 [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_eq -> eq [0]
   encode_0 -> 0 [0]
   encode_true -> true [0]
   encode_s -> s [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_union -> union [0]
   encode_empty -> empty [0]
   encode_edge -> edge [0]
   encode_reach -> reach [0]
   encode_if_reach_1 -> if_reach_1 [0]
   encode_if_reach_2 -> if_reach_2 [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_eq -> null_encode_eq [0]
   encode_0 -> null_encode_0 [0]
   encode_true -> null_encode_true [0]
   encode_s -> null_encode_s [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_union -> null_encode_union [0]
   encode_empty -> null_encode_empty [0]
   encode_edge -> null_encode_edge [0]
   encode_reach -> null_encode_reach [0]
   encode_if_reach_1 -> null_encode_if_reach_1 [0]
   encode_if_reach_2 -> null_encode_if_reach_2 [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_filter -> null_encode_filter [0]
   encode_filter2 -> null_encode_filter2 [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
c_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encArg :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
cons_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encArg :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app

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

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

(24)
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:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(eq, c_app(s, x)), 0) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> true [1]
   app(c_app(eq, 0), 0) -> true [1]
   app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(c_app(eq, x), y) [1]
   app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(null_app, y) [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(c_app(filter, f), xs) [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(null_app, xs) [1]
   app(c_app(or, false), y) -> y [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(c_app(reach, x), y), i), app(app(c_app(edge, u), v), h)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(c_app(reach, x), y), i), app(app(null_app, v), h)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(null_app, y), i), app(app(c_app(edge, u), v), h)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(null_app, y), i), app(app(null_app, v), h)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(c_app(reach, x), y), i), h)), app(app(app(c_app(reach, v), y), app(c_app(union, i), h)), empty)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(c_app(reach, x), y), i), h)), app(app(app(c_app(reach, v), y), app(null_app, h)), empty)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(c_app(reach, x), y), i), h)), app(app(app(null_app, y), app(c_app(union, i), h)), empty)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(c_app(reach, x), y), i), h)), app(app(app(null_app, y), app(null_app, h)), empty)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(null_app, y), i), h)), app(app(app(c_app(reach, v), y), app(c_app(union, i), h)), empty)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(null_app, y), i), h)), app(app(app(c_app(reach, v), y), app(null_app, h)), empty)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(null_app, y), i), h)), app(app(app(null_app, y), app(c_app(union, i), h)), empty)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(null_app, y), i), h)), app(app(app(null_app, y), app(null_app, h)), empty)) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(c_app(reach, x), y), empty), h) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(c_app(eq, y), v)), x), y), app(app(c_app(edge, u), v), i)), h) [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(c_app(eq, y), v)), x), y), app(app(null_app, v), i)), h) [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(null_app, v)), x), y), app(app(c_app(edge, u), v), i)), h) [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(null_app, v)), x), y), app(app(null_app, v), i)), h) [1]
   app(c_app(or, true), y) -> true [1]
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(c_app(cons, x), app(c_app(filter, f), xs)) [1]
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(c_app(cons, x), app(null_app, xs)) [1]
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(null_app, app(c_app(filter, f), xs)) [1]
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(null_app, app(null_app, xs)) [1]
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(c_app(edge, x), y), app(c_app(union, i), h)) [1]
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(c_app(edge, x), y), app(null_app, h)) [1]
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(null_app, y), app(c_app(union, i), h)) [1]
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(null_app, y), app(null_app, h)) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(union, empty), h) -> h [1]
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(c_app(eq, x), u)), x), y), app(app(c_app(edge, u), v), i)), h) [1]
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(c_app(eq, x), u)), x), y), app(app(null_app, v), i)), h) [1]
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(null_app, u)), x), y), app(app(c_app(edge, u), v), i)), h) [1]
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(null_app, u)), x), y), app(app(null_app, v), i)), h) [1]
   app(c_app(eq, 0), c_app(s, x)) -> false [1]
   encArg(eq) -> eq [0]
   encArg(0) -> 0 [0]
   encArg(true) -> true [0]
   encArg(s) -> s [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(union) -> union [0]
   encArg(empty) -> empty [0]
   encArg(edge) -> edge [0]
   encArg(reach) -> reach [0]
   encArg(if_reach_1) -> if_reach_1 [0]
   encArg(if_reach_2) -> if_reach_2 [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_eq -> eq [0]
   encode_0 -> 0 [0]
   encode_true -> true [0]
   encode_s -> s [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_union -> union [0]
   encode_empty -> empty [0]
   encode_edge -> edge [0]
   encode_reach -> reach [0]
   encode_if_reach_1 -> if_reach_1 [0]
   encode_if_reach_2 -> if_reach_2 [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_eq -> null_encode_eq [0]
   encode_0 -> null_encode_0 [0]
   encode_true -> null_encode_true [0]
   encode_s -> null_encode_s [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_union -> null_encode_union [0]
   encode_empty -> null_encode_empty [0]
   encode_edge -> null_encode_edge [0]
   encode_reach -> null_encode_reach [0]
   encode_if_reach_1 -> null_encode_if_reach_1 [0]
   encode_if_reach_2 -> null_encode_if_reach_2 [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_filter -> null_encode_filter [0]
   encode_filter2 -> null_encode_filter2 [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
c_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encArg :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
cons_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encArg :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app

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

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

   map => 10
   cons => 1
   eq => 4
   s => 14
   0 => 0
   false => 5
   if_reach_2 => 9
   true => 15
   edge => 2
   filter2 => 7
   filter => 6
   or => 12
   if_reach_1 => 8
   reach => 13
   union => 16
   empty => 3
   nil => 11
   null_encArg => 0
   null_encode_app => 0
   null_encode_eq => 0
   null_encode_0 => 0
   null_encode_true => 0
   null_encode_s => 0
   null_encode_false => 0
   null_encode_or => 0
   null_encode_union => 0
   null_encode_empty => 0
   null_encode_edge => 0
   null_encode_reach => 0
   null_encode_if_reach_1 => 0
   null_encode_if_reach_2 => 0
   null_encode_map => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_filter => 0
   null_encode_filter2 => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> h :|: z' = h, z = 1 + 16 + 3, h >= 0
   app(z, z') -{ 1 }-> y :|: z = 1 + 12 + 5, y >= 0, z' = y
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(0, v)), x), y), app(app(0, v), i)), h) :|: z' = h, v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(0, v)), x), y), app(app(1 + 2 + u, v), i)), h) :|: z' = h, v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(1 + 4 + y, v)), x), y), app(app(0, v), i)), h) :|: z' = h, v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(1 + 4 + y, v)), x), y), app(app(1 + 2 + u, v), i)), h) :|: z' = h, v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(0, u)), x), y), app(app(0, v), i)), h) :|: z' = h, v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(0, u)), x), y), app(app(1 + 2 + u, v), i)), h) :|: z' = h, v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(1 + 4 + x, u)), x), y), app(app(0, v), i)), h) :|: z' = h, v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(1 + 4 + x, u)), x), y), app(app(1 + 2 + u, v), i)), h) :|: z' = h, v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(7, app(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 6 + f, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(0, y), i), app(app(0, v), h)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(0, y), i), app(app(1 + 2 + u, v), h)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(1 + 13 + x, y), i), app(app(0, v), h)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(1 + 13 + x, y), i), app(app(1 + 2 + u, v), h)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(0, y), i), h)), app(app(app(0, y), app(0, h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(0, y), i), h)), app(app(app(0, y), app(1 + 16 + i, h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(0, y), i), h)), app(app(app(1 + 13 + v, y), app(0, h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(0, y), i), h)), app(app(app(1 + 13 + v, y), app(1 + 16 + i, h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(1 + 13 + x, y), i), h)), app(app(app(0, y), app(0, h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(1 + 13 + x, y), i), h)), app(app(app(0, y), app(1 + 16 + i, h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(1 + 13 + x, y), i), h)), app(app(app(1 + 13 + v, y), app(0, h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(1 + 13 + x, y), i), h)), app(app(app(1 + 13 + v, y), app(1 + 16 + i, h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(1, app(f, x)), app(app(10, f), xs)) :|: f >= 0, xs >= 0, z = 1 + 10 + f, x >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(0, y), app(0, h)) :|: z' = h, x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), h >= 0
   app(z, z') -{ 1 }-> app(app(0, y), app(1 + 16 + i, h)) :|: z' = h, x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), h >= 0
   app(z, z') -{ 1 }-> app(app(1 + 2 + x, y), app(0, h)) :|: z' = h, x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), h >= 0
   app(z, z') -{ 1 }-> app(app(1 + 2 + x, y), app(1 + 16 + i, h)) :|: z' = h, x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), h >= 0
   app(z, z') -{ 1 }-> app(0, xs) :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(0, y) :|: z' = 1 + 14 + y, x >= 0, y >= 0, z = 1 + 4 + (1 + 14 + x)
   app(z, z') -{ 1 }-> app(0, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> app(0, app(1 + 6 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> app(1 + 6 + f, xs) :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(1 + 4 + x, y) :|: z' = 1 + 14 + y, x >= 0, y >= 0, z = 1 + 4 + (1 + 14 + x)
   app(z, z') -{ 1 }-> app(1 + 1 + x, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> app(1 + 1 + x, app(1 + 6 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> 5 :|: x >= 0, z = 1 + 4 + (1 + 14 + x), z' = 0
   app(z, z') -{ 1 }-> 5 :|: z' = h, x >= 0, y >= 0, h >= 0, z = 1 + (1 + (1 + 13 + x) + y) + 3
   app(z, z') -{ 1 }-> 5 :|: z' = 1 + 14 + x, x >= 0, z = 1 + 4 + 0
   app(z, z') -{ 1 }-> 15 :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> 15 :|: z = 1 + 4 + 0, z' = 0
   app(z, z') -{ 1 }-> 15 :|: z = 1 + 12 + 15, y >= 0, z' = y
   app(z, z') -{ 1 }-> 11 :|: f >= 0, z = 1 + 10 + f, z' = 11
   app(z, z') -{ 1 }-> 11 :|: f >= 0, z' = 11, z = 1 + 6 + f
   app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 9 :|: z = 9
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 16 :|: z = 16
   encArg(z) -{ 0 }-> 15 :|: z = 15
   encArg(z) -{ 0 }-> 14 :|: z = 14
   encArg(z) -{ 0 }-> 13 :|: z = 13
   encArg(z) -{ 0 }-> 12 :|: z = 12
   encArg(z) -{ 0 }-> 11 :|: z = 11
   encArg(z) -{ 0 }-> 10 :|: z = 10
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_0 -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_edge -{ 0 }-> 2 :|: 
   encode_edge -{ 0 }-> 0 :|: 
   encode_empty -{ 0 }-> 3 :|: 
   encode_empty -{ 0 }-> 0 :|: 
   encode_eq -{ 0 }-> 4 :|: 
   encode_eq -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 5 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 6 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 7 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_if_reach_1 -{ 0 }-> 8 :|: 
   encode_if_reach_1 -{ 0 }-> 0 :|: 
   encode_if_reach_2 -{ 0 }-> 9 :|: 
   encode_if_reach_2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 10 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 11 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_or -{ 0 }-> 12 :|: 
   encode_or -{ 0 }-> 0 :|: 
   encode_reach -{ 0 }-> 13 :|: 
   encode_reach -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 14 :|: 
   encode_s -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 15 :|: 
   encode_true -{ 0 }-> 0 :|: 
   encode_union -{ 0 }-> 16 :|: 
   encode_union -{ 0 }-> 0 :|: 


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

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

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

   app(z, z') -{ 1 }-> z' :|: z = 1 + 12 + 5, z' >= 0
   app(z, z') -{ 1 }-> z' :|: z = 1 + 16 + 3, z' >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(0, v)), x), y), app(app(0, v), i)), z') :|: v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(0, v)), x), y), app(app(1 + 2 + u, v), i)), z') :|: v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(1 + 4 + y, v)), x), y), app(app(0, v), i)), z') :|: v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(1 + 4 + y, v)), x), y), app(app(1 + 2 + u, v), i)), z') :|: v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(0, u)), x), y), app(app(0, v), i)), z') :|: v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(0, u)), x), y), app(app(1 + 2 + u, v), i)), z') :|: v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(1 + 4 + x, u)), x), y), app(app(0, v), i)), z') :|: v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(1 + 4 + x, u)), x), y), app(app(1 + 2 + u, v), i)), z') :|: v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(7, app(z - 7, x)), z - 7), x), xs) :|: z - 7 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(0, y), i), app(app(0, v), z')) :|: v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(0, y), i), app(app(1 + 2 + u, v), z')) :|: v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(1 + 13 + x, y), i), app(app(0, v), z')) :|: v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(1 + 13 + x, y), i), app(app(1 + 2 + u, v), z')) :|: v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(0, y), i), z')), app(app(app(0, y), app(0, z')), 3)) :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(0, y), i), z')), app(app(app(0, y), app(1 + 16 + i, z')), 3)) :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(0, y), i), z')), app(app(app(1 + 13 + v, y), app(0, z')), 3)) :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(0, y), i), z')), app(app(app(1 + 13 + v, y), app(1 + 16 + i, z')), 3)) :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(1 + 13 + x, y), i), z')), app(app(app(0, y), app(0, z')), 3)) :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(1 + 13 + x, y), i), z')), app(app(app(0, y), app(1 + 16 + i, z')), 3)) :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(1 + 13 + x, y), i), z')), app(app(app(1 + 13 + v, y), app(0, z')), 3)) :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(12, app(app(app(1 + 13 + x, y), i), z')), app(app(app(1 + 13 + v, y), app(1 + 16 + i, z')), 3)) :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(1, app(z - 11, x)), app(app(10, z - 11), xs)) :|: z - 11 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(0, y), app(0, z')) :|: x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), z' >= 0
   app(z, z') -{ 1 }-> app(app(0, y), app(1 + 16 + i, z')) :|: x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), z' >= 0
   app(z, z') -{ 1 }-> app(app(1 + 2 + x, y), app(0, z')) :|: x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), z' >= 0
   app(z, z') -{ 1 }-> app(app(1 + 2 + x, y), app(1 + 16 + i, z')) :|: x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), z' >= 0
   app(z, z') -{ 1 }-> app(0, z') :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, z' >= 0, x >= 0
   app(z, z') -{ 1 }-> app(0, app(0, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> app(0, app(1 + 6 + f, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> app(0, z' - 15) :|: z - 20 >= 0, z' - 15 >= 0
   app(z, z') -{ 1 }-> app(1 + 6 + f, z') :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, z' >= 0, x >= 0
   app(z, z') -{ 1 }-> app(1 + 4 + (z - 20), z' - 15) :|: z - 20 >= 0, z' - 15 >= 0
   app(z, z') -{ 1 }-> app(1 + 1 + x, app(0, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> app(1 + 1 + x, app(1 + 6 + f, z')) :|: f >= 0, z' >= 0, x >= 0, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> 5 :|: z - 20 >= 0, z' = 0
   app(z, z') -{ 1 }-> 5 :|: x >= 0, y >= 0, z' >= 0, z = 1 + (1 + (1 + 13 + x) + y) + 3
   app(z, z') -{ 1 }-> 5 :|: z' - 15 >= 0, z = 1 + 4 + 0
   app(z, z') -{ 1 }-> 15 :|: v >= 0, z = 1 + (1 + (1 + (1 + 9 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, z' >= 0, u >= 0
   app(z, z') -{ 1 }-> 15 :|: z = 1 + 4 + 0, z' = 0
   app(z, z') -{ 1 }-> 15 :|: z = 1 + 12 + 15, z' >= 0
   app(z, z') -{ 1 }-> 11 :|: z - 11 >= 0, z' = 11
   app(z, z') -{ 1 }-> 11 :|: z - 7 >= 0, z' = 11
   app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   app(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 9 :|: z = 9
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 16 :|: z = 16
   encArg(z) -{ 0 }-> 15 :|: z = 15
   encArg(z) -{ 0 }-> 14 :|: z = 14
   encArg(z) -{ 0 }-> 13 :|: z = 13
   encArg(z) -{ 0 }-> 12 :|: z = 12
   encArg(z) -{ 0 }-> 11 :|: z = 11
   encArg(z) -{ 0 }-> 10 :|: z = 10
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_edge -{ 0 }-> 2 :|: 
   encode_edge -{ 0 }-> 0 :|: 
   encode_empty -{ 0 }-> 3 :|: 
   encode_empty -{ 0 }-> 0 :|: 
   encode_eq -{ 0 }-> 4 :|: 
   encode_eq -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 5 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 6 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 7 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_if_reach_1 -{ 0 }-> 8 :|: 
   encode_if_reach_1 -{ 0 }-> 0 :|: 
   encode_if_reach_2 -{ 0 }-> 9 :|: 
   encode_if_reach_2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 10 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 11 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_or -{ 0 }-> 12 :|: 
   encode_or -{ 0 }-> 0 :|: 
   encode_reach -{ 0 }-> 13 :|: 
   encode_reach -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 14 :|: 
   encode_s -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 15 :|: 
   encode_true -{ 0 }-> 0 :|: 
   encode_union -{ 0 }-> 16 :|: 
   encode_union -{ 0 }-> 0 :|: 


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

(29) 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:

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_eq -> null_encode_eq [0]
   encode_0 -> null_encode_0 [0]
   encode_true -> null_encode_true [0]
   encode_s -> null_encode_s [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_union -> null_encode_union [0]
   encode_empty -> null_encode_empty [0]
   encode_edge -> null_encode_edge [0]
   encode_reach -> null_encode_reach [0]
   encode_if_reach_1 -> null_encode_if_reach_1 [0]
   encode_if_reach_2 -> null_encode_if_reach_2 [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_filter -> null_encode_filter [0]
   encode_filter2 -> null_encode_filter2 [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_eq, null_encode_0, null_encode_true, null_encode_s, null_encode_false, null_encode_or, null_encode_union, null_encode_empty, null_encode_edge, null_encode_reach, null_encode_if_reach_1, null_encode_if_reach_2, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_app

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

(30)
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:

   app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1]
   app(c_app(eq, c_app(s, x)), 0) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> true [1]
   app(c_app(eq, 0), 0) -> true [1]
   app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) [1]
   app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(or, false), y) -> y [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h)) [1]
   app(c_app(c_app(c_app(c_app(if_reach_2, false), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty)) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(c_app(c_app(reach, x), y), empty), h) -> false [1]
   app(c_app(c_app(c_app(c_app(if_reach_1, true), x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h) [1]
   app(c_app(or, true), y) -> true [1]
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1]
   app(c_app(union, c_app(c_app(c_app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h)) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(union, empty), h) -> h [1]
   app(c_app(c_app(c_app(reach, x), y), c_app(c_app(c_app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h) [1]
   app(c_app(eq, 0), c_app(s, x)) -> false [1]
   encArg(eq) -> eq [0]
   encArg(0) -> 0 [0]
   encArg(true) -> true [0]
   encArg(s) -> s [0]
   encArg(false) -> false [0]
   encArg(or) -> or [0]
   encArg(union) -> union [0]
   encArg(empty) -> empty [0]
   encArg(edge) -> edge [0]
   encArg(reach) -> reach [0]
   encArg(if_reach_1) -> if_reach_1 [0]
   encArg(if_reach_2) -> if_reach_2 [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0]
   encode_eq -> eq [0]
   encode_0 -> 0 [0]
   encode_true -> true [0]
   encode_s -> s [0]
   encode_false -> false [0]
   encode_or -> or [0]
   encode_union -> union [0]
   encode_empty -> empty [0]
   encode_edge -> edge [0]
   encode_reach -> reach [0]
   encode_if_reach_1 -> if_reach_1 [0]
   encode_if_reach_2 -> if_reach_2 [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_eq -> null_encode_eq [0]
   encode_0 -> null_encode_0 [0]
   encode_true -> null_encode_true [0]
   encode_s -> null_encode_s [0]
   encode_false -> null_encode_false [0]
   encode_or -> null_encode_or [0]
   encode_union -> null_encode_union [0]
   encode_empty -> null_encode_empty [0]
   encode_edge -> null_encode_edge [0]
   encode_reach -> null_encode_reach [0]
   encode_if_reach_1 -> null_encode_if_reach_1 [0]
   encode_if_reach_2 -> null_encode_if_reach_2 [0]
   encode_map -> null_encode_map [0]
   encode_nil -> null_encode_nil [0]
   encode_cons -> null_encode_cons [0]
   encode_filter -> null_encode_filter [0]
   encode_filter2 -> null_encode_filter2 [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
c_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encArg :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
cons_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
encode_filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encArg :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_eq :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_0 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_true :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_s :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_false :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_or :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_union :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_empty :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_edge :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_reach :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_if_reach_1 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_if_reach_2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_map :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_nil :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_cons :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_filter :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_encode_filter2 :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app
null_app :: map:c_app:cons:eq:s:0:false:if_reach_2:true:edge:filter2:filter:or:if_reach_1:reach:union:empty:nil:cons_app:null_encArg:null_encode_app:null_encode_eq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_or:null_encode_union:null_encode_empty:null_encode_edge:null_encode_reach:null_encode_if_reach_1:null_encode_if_reach_2:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app

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

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

   map => 10
   cons => 1
   eq => 4
   s => 14
   0 => 0
   false => 5
   if_reach_2 => 9
   true => 15
   edge => 2
   filter2 => 7
   filter => 6
   or => 12
   if_reach_1 => 8
   reach => 13
   union => 16
   empty => 3
   nil => 11
   null_encArg => 0
   null_encode_app => 0
   null_encode_eq => 0
   null_encode_0 => 0
   null_encode_true => 0
   null_encode_s => 0
   null_encode_false => 0
   null_encode_or => 0
   null_encode_union => 0
   null_encode_empty => 0
   null_encode_edge => 0
   null_encode_reach => 0
   null_encode_if_reach_1 => 0
   null_encode_if_reach_2 => 0
   null_encode_map => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_filter => 0
   null_encode_filter2 => 0
   null_app => 0

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

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

   app(z, z') -{ 1 }-> h :|: z' = h, z = 1 + 16 + 3, h >= 0
   app(z, z') -{ 1 }-> y :|: z = 1 + 12 + 5, y >= 0, z' = y
   app(z, z') -{ 1 }-> app(app(app(app(app(9, app(app(4, y), v)), x), y), app(app(app(2, u), v), i)), h) :|: z' = h, v >= 0, x >= 0, y >= 0, i >= 0, z = 1 + (1 + (1 + (1 + 8 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(app(8, app(app(4, x), u)), x), y), app(app(app(2, u), v), i)), h) :|: z' = h, v >= 0, z = 1 + (1 + (1 + 13 + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(app(7, app(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 6 + f, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(app(app(13, x), y), i), app(app(app(2, u), v), h)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 8 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(app(2, x), y), app(app(16, i), h)) :|: z' = h, x >= 0, y >= 0, i >= 0, z = 1 + 16 + (1 + (1 + (1 + 2 + x) + y) + i), h >= 0
   app(z, z') -{ 1 }-> app(app(6, f), xs) :|: f >= 0, z = 1 + (1 + (1 + 7 + 5) + f) + x, xs >= 0, x >= 0, z' = xs
   app(z, z') -{ 1 }-> app(app(4, x), y) :|: z' = 1 + 14 + y, x >= 0, y >= 0, z = 1 + 4 + (1 + 14 + x)
   app(z, z') -{ 1 }-> app(app(12, app(app(app(app(13, x), y), i), h)), app(app(app(app(13, v), y), app(app(16, i), h)), 3)) :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 5) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> app(app(1, x), app(app(6, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z' = xs, z = 1 + (1 + (1 + 7 + 15) + f) + x
   app(z, z') -{ 1 }-> app(app(1, app(f, x)), app(app(10, f), xs)) :|: f >= 0, xs >= 0, z = 1 + 10 + f, x >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> 5 :|: x >= 0, z = 1 + 4 + (1 + 14 + x), z' = 0
   app(z, z') -{ 1 }-> 5 :|: z' = h, x >= 0, y >= 0, h >= 0, z = 1 + (1 + (1 + 13 + x) + y) + 3
   app(z, z') -{ 1 }-> 5 :|: z' = 1 + 14 + x, x >= 0, z = 1 + 4 + 0
   app(z, z') -{ 1 }-> 15 :|: z' = h, v >= 0, z = 1 + (1 + (1 + (1 + 9 + 15) + x) + y) + (1 + (1 + (1 + 2 + u) + v) + i), x >= 0, y >= 0, i >= 0, h >= 0, u >= 0
   app(z, z') -{ 1 }-> 15 :|: z = 1 + 4 + 0, z' = 0
   app(z, z') -{ 1 }-> 15 :|: z = 1 + 12 + 15, y >= 0, z' = y
   app(z, z') -{ 1 }-> 11 :|: f >= 0, z = 1 + 10 + f, z' = 11
   app(z, z') -{ 1 }-> 11 :|: f >= 0, z' = 11, z = 1 + 6 + f
   app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 9 :|: z = 9
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 16 :|: z = 16
   encArg(z) -{ 0 }-> 15 :|: z = 15
   encArg(z) -{ 0 }-> 14 :|: z = 14
   encArg(z) -{ 0 }-> 13 :|: z = 13
   encArg(z) -{ 0 }-> 12 :|: z = 12
   encArg(z) -{ 0 }-> 11 :|: z = 11
   encArg(z) -{ 0 }-> 10 :|: z = 10
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_0 -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_edge -{ 0 }-> 2 :|: 
   encode_edge -{ 0 }-> 0 :|: 
   encode_empty -{ 0 }-> 3 :|: 
   encode_empty -{ 0 }-> 0 :|: 
   encode_eq -{ 0 }-> 4 :|: 
   encode_eq -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 5 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 6 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 7 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_if_reach_1 -{ 0 }-> 8 :|: 
   encode_if_reach_1 -{ 0 }-> 0 :|: 
   encode_if_reach_2 -{ 0 }-> 9 :|: 
   encode_if_reach_2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 10 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 11 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_or -{ 0 }-> 12 :|: 
   encode_or -{ 0 }-> 0 :|: 
   encode_reach -{ 0 }-> 13 :|: 
   encode_reach -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 14 :|: 
   encode_s -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 15 :|: 
   encode_true -{ 0 }-> 0 :|: 
   encode_union -{ 0 }-> 16 :|: 
   encode_union -{ 0 }-> 0 :|: 

Only complete derivations are relevant for the runtime complexity.

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

(33) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS to CDT
----------------------------------------

(34)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   ENCARG(eq) -> c
   ENCARG(0) -> c1
   ENCARG(true) -> c2
   ENCARG(s) -> c3
   ENCARG(false) -> c4
   ENCARG(or) -> c5
   ENCARG(union) -> c6
   ENCARG(empty) -> c7
   ENCARG(edge) -> c8
   ENCARG(reach) -> c9
   ENCARG(if_reach_1) -> c10
   ENCARG(if_reach_2) -> c11
   ENCARG(map) -> c12
   ENCARG(nil) -> c13
   ENCARG(cons) -> c14
   ENCARG(filter) -> c15
   ENCARG(filter2) -> c16
   ENCARG(cons_app(z0, z1)) -> c17(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c18(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_EQ -> c19
   ENCODE_0 -> c20
   ENCODE_TRUE -> c21
   ENCODE_S -> c22
   ENCODE_FALSE -> c23
   ENCODE_OR -> c24
   ENCODE_UNION -> c25
   ENCODE_EMPTY -> c26
   ENCODE_EDGE -> c27
   ENCODE_REACH -> c28
   ENCODE_IF_REACH_1 -> c29
   ENCODE_IF_REACH_2 -> c30
   ENCODE_MAP -> c31
   ENCODE_NIL -> c32
   ENCODE_CONS -> c33
   ENCODE_FILTER -> c34
   ENCODE_FILTER2 -> c35
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1), APP(eq, z0))
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(app(edge, z0), z1), app(app(union, z2), z3)), APP(app(edge, z0), z1), APP(edge, z0), APP(app(union, z2), z3), APP(union, z2))
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), APP(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), APP(app(if_reach_1, app(app(eq, z0), z2)), z0), APP(if_reach_1, app(app(eq, z0), z2)), APP(app(eq, z0), z2), APP(eq, z0), APP(app(app(edge, z2), z3), z4), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), APP(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), APP(app(if_reach_2, app(app(eq, z1), z3)), z0), APP(if_reach_2, app(app(eq, z1), z3)), APP(app(eq, z1), z3), APP(eq, z1), APP(app(app(edge, z2), z3), z4), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)), APP(app(app(reach, z0), z1), z4), APP(app(reach, z0), z1), APP(reach, z0), APP(app(app(edge, z2), z3), z5), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(or, app(app(app(app(reach, z0), z1), z4), z5)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(reach, z0), z1), z4), APP(app(reach, z0), z1), APP(reach, z0), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(app(reach, z3), z1), app(app(union, z4), z5)), APP(app(reach, z3), z1), APP(reach, z3), APP(app(union, z4), z5), APP(union, z4))
   APP(app(map, z0), nil) -> c50
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0))
   APP(app(filter, z0), nil) -> c52
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1), APP(eq, z0))
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(app(edge, z0), z1), app(app(union, z2), z3)), APP(app(edge, z0), z1), APP(edge, z0), APP(app(union, z2), z3), APP(union, z2))
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), APP(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), APP(app(if_reach_1, app(app(eq, z0), z2)), z0), APP(if_reach_1, app(app(eq, z0), z2)), APP(app(eq, z0), z2), APP(eq, z0), APP(app(app(edge, z2), z3), z4), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), APP(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), APP(app(if_reach_2, app(app(eq, z1), z3)), z0), APP(if_reach_2, app(app(eq, z1), z3)), APP(app(eq, z1), z3), APP(eq, z1), APP(app(app(edge, z2), z3), z4), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)), APP(app(app(reach, z0), z1), z4), APP(app(reach, z0), z1), APP(reach, z0), APP(app(app(edge, z2), z3), z5), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(or, app(app(app(app(reach, z0), z1), z4), z5)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(reach, z0), z1), z4), APP(app(reach, z0), z1), APP(reach, z0), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(app(reach, z3), z1), app(app(union, z4), z5)), APP(app(reach, z3), z1), APP(reach, z3), APP(app(union, z4), z5), APP(union, z4))
   APP(app(map, z0), nil) -> c50
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0))
   APP(app(filter, z0), nil) -> c52
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_eq, encode_0, encode_true, encode_s, encode_false, encode_or, encode_union, encode_empty, encode_edge, encode_reach, encode_if_reach_1, encode_if_reach_2, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, ENCODE_EQ, ENCODE_0, ENCODE_TRUE, ENCODE_S, ENCODE_FALSE, ENCODE_OR, ENCODE_UNION, ENCODE_EMPTY, ENCODE_EDGE, ENCODE_REACH, ENCODE_IF_REACH_1, ENCODE_IF_REACH_2, ENCODE_MAP, ENCODE_NIL, ENCODE_CONS, ENCODE_FILTER, ENCODE_FILTER2, APP_2

Compound Symbols:   c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17_3, c18_3, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39_2, c40, c41, c42, c43_5, c44, c45_10, c46_10, c47_7, c48, c49_12, c50, c51_5, c52, c53_5, c54_4, c55_2


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

(35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 34 trailing nodes:
   ENCARG(map) -> c12
   ENCARG(reach) -> c9
   ENCARG(or) -> c5
   ENCODE_IF_REACH_2 -> c30
   ENCODE_S -> c22
   ENCARG(if_reach_1) -> c10
   ENCODE_REACH -> c28
   ENCODE_EMPTY -> c26
   ENCODE_EQ -> c19
   ENCODE_FILTER2 -> c35
   ENCODE_UNION -> c25
   ENCODE_FILTER -> c34
   ENCODE_0 -> c20
   ENCODE_FALSE -> c23
   ENCARG(true) -> c2
   ENCARG(edge) -> c8
   ENCARG(filter2) -> c16
   ENCARG(nil) -> c13
   ENCARG(0) -> c1
   ENCARG(eq) -> c
   ENCODE_MAP -> c31
   ENCODE_IF_REACH_1 -> c29
   ENCARG(union) -> c6
   ENCARG(false) -> c4
   ENCARG(if_reach_2) -> c11
   ENCARG(filter) -> c15
   ENCODE_TRUE -> c21
   ENCARG(s) -> c3
   ENCODE_EDGE -> c27
   ENCARG(empty) -> c7
   ENCODE_CONS -> c33
   ENCODE_OR -> c24
   ENCODE_NIL -> c32
   ENCARG(cons) -> c14

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   ENCARG(cons_app(z0, z1)) -> c17(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c18(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1), APP(eq, z0))
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(app(edge, z0), z1), app(app(union, z2), z3)), APP(app(edge, z0), z1), APP(edge, z0), APP(app(union, z2), z3), APP(union, z2))
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), APP(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), APP(app(if_reach_1, app(app(eq, z0), z2)), z0), APP(if_reach_1, app(app(eq, z0), z2)), APP(app(eq, z0), z2), APP(eq, z0), APP(app(app(edge, z2), z3), z4), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), APP(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), APP(app(if_reach_2, app(app(eq, z1), z3)), z0), APP(if_reach_2, app(app(eq, z1), z3)), APP(app(eq, z1), z3), APP(eq, z1), APP(app(app(edge, z2), z3), z4), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)), APP(app(app(reach, z0), z1), z4), APP(app(reach, z0), z1), APP(reach, z0), APP(app(app(edge, z2), z3), z5), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(or, app(app(app(app(reach, z0), z1), z4), z5)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(reach, z0), z1), z4), APP(app(reach, z0), z1), APP(reach, z0), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(app(reach, z3), z1), app(app(union, z4), z5)), APP(app(reach, z3), z1), APP(reach, z3), APP(app(union, z4), z5), APP(union, z4))
   APP(app(map, z0), nil) -> c50
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0))
   APP(app(filter, z0), nil) -> c52
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1), APP(eq, z0))
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(app(edge, z0), z1), app(app(union, z2), z3)), APP(app(edge, z0), z1), APP(edge, z0), APP(app(union, z2), z3), APP(union, z2))
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), APP(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), APP(app(if_reach_1, app(app(eq, z0), z2)), z0), APP(if_reach_1, app(app(eq, z0), z2)), APP(app(eq, z0), z2), APP(eq, z0), APP(app(app(edge, z2), z3), z4), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), APP(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), APP(app(if_reach_2, app(app(eq, z1), z3)), z0), APP(if_reach_2, app(app(eq, z1), z3)), APP(app(eq, z1), z3), APP(eq, z1), APP(app(app(edge, z2), z3), z4), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)), APP(app(app(reach, z0), z1), z4), APP(app(reach, z0), z1), APP(reach, z0), APP(app(app(edge, z2), z3), z5), APP(app(edge, z2), z3), APP(edge, z2))
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(or, app(app(app(app(reach, z0), z1), z4), z5)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(reach, z0), z1), z4), APP(app(reach, z0), z1), APP(reach, z0), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(app(reach, z3), z1), app(app(union, z4), z5)), APP(app(reach, z3), z1), APP(reach, z3), APP(app(union, z4), z5), APP(union, z4))
   APP(app(map, z0), nil) -> c50
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0))
   APP(app(filter, z0), nil) -> c52
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_eq, encode_0, encode_true, encode_s, encode_false, encode_or, encode_union, encode_empty, encode_edge, encode_reach, encode_if_reach_1, encode_if_reach_2, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c17_3, c18_3, c36, c37, c38, c39_2, c40, c41, c42, c43_5, c44, c45_10, c46_10, c47_7, c48, c49_12, c50, c51_5, c52, c53_5, c54_4, c55_2


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

(37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 45 trailing tuple parts
----------------------------------------

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   ENCARG(cons_app(z0, z1)) -> c17(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c18(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_eq, encode_0, encode_true, encode_s, encode_false, encode_or, encode_union, encode_empty, encode_edge, encode_reach, encode_if_reach_1, encode_if_reach_2, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c17_3, c18_3, c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c45_2, c46_2, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1


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

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   ENCARG(cons_app(z0, z1)) -> c17(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCODE_APP(z0, z1) -> c(ENCARG(z0))
   ENCODE_APP(z0, z1) -> c(ENCARG(z1))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_eq, encode_0, encode_true, encode_s, encode_false, encode_or, encode_union, encode_empty, encode_edge, encode_reach, encode_if_reach_1, encode_if_reach_2, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c17_3, c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c45_2, c46_2, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1, c_1


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

(41) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ENCODE_APP(z0, z1) -> c(ENCARG(z0))
   ENCODE_APP(z0, z1) -> c(ENCARG(z1))

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   ENCARG(cons_app(z0, z1)) -> c17(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_eq, encode_0, encode_true, encode_s, encode_false, encode_or, encode_union, encode_empty, encode_edge, encode_reach, encode_if_reach_1, encode_if_reach_2, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c17_3, c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c45_2, c46_2, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1, c_1


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

(43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_eq -> eq
   encode_0 -> 0
   encode_true -> true
   encode_s -> s
   encode_false -> false
   encode_or -> or
   encode_union -> union
   encode_empty -> empty
   encode_edge -> edge
   encode_reach -> reach
   encode_if_reach_1 -> if_reach_1
   encode_if_reach_2 -> if_reach_2
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   ENCARG(cons_app(z0, z1)) -> c17(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c17_3, c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c45_2, c46_2, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1, c_1


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

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c17(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0), ENCARG(eq))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0), ENCARG(s))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0), ENCARG(or))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0), ENCARG(union))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0), ENCARG(empty))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0), ENCARG(edge))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0), ENCARG(reach))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0), ENCARG(if_reach_1))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0), ENCARG(if_reach_2))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(eq, x1)) -> c17(APP(eq, encArg(x1)), ENCARG(eq), ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(APP(or, encArg(x1)), ENCARG(or), ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(APP(union, encArg(x1)), ENCARG(union), ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(APP(empty, encArg(x1)), ENCARG(empty), ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(APP(edge, encArg(x1)), ENCARG(edge), ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(APP(reach, encArg(x1)), ENCARG(reach), ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(APP(if_reach_1, encArg(x1)), ENCARG(if_reach_1), ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(APP(if_reach_2, encArg(x1)), ENCARG(if_reach_2), ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0), ENCARG(eq))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0), ENCARG(s))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0), ENCARG(or))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0), ENCARG(union))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0), ENCARG(empty))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0), ENCARG(edge))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0), ENCARG(reach))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0), ENCARG(if_reach_1))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0), ENCARG(if_reach_2))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(eq, x1)) -> c17(APP(eq, encArg(x1)), ENCARG(eq), ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(APP(or, encArg(x1)), ENCARG(or), ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(APP(union, encArg(x1)), ENCARG(union), ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(APP(empty, encArg(x1)), ENCARG(empty), ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(APP(edge, encArg(x1)), ENCARG(edge), ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(APP(reach, encArg(x1)), ENCARG(reach), ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(APP(if_reach_1, encArg(x1)), ENCARG(if_reach_1), ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(APP(if_reach_2, encArg(x1)), ENCARG(if_reach_2), ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c45_2, c46_2, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1, c_1, c17_3


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

(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 51 trailing tuple parts
----------------------------------------

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c45_2, c46_2, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1, c_1, c17_3, c17_2, c17_1


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z0), z2)) by 
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c46_2, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1, c_1, c17_3, c17_2, c17_1, c45_2


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(eq, z1), z3)) by 
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1, c_1, c17_3, c17_2, c17_1, c45_2, c46_2


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

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c49_4, c51_2, c53_2, c54_1, c55_1, c_1, c17_3, c17_2, c17_1, c45_2, c46_2, c1_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c49(APP(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty)), APP(app(app(app(reach, z0), z1), z4), z5), APP(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty), APP(app(union, z4), z5)) by 
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c53_2, c54_1, c55_1, c_1, c17_3, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c53(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) by 
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(app(app(filter2, app(app(app(edge, z0), z1), app(app(union, z2), z3))), app(union, app(app(app(edge, z0), z1), z2))), z3), x2), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(app(app(filter2, app(app(app(edge, z0), z1), app(app(union, z2), z3))), app(union, app(app(app(edge, z0), z1), z2))), z3), x2), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(app(app(filter2, app(app(app(edge, z0), z1), app(app(union, z2), z3))), app(union, app(app(app(edge, z0), z1), z2))), z3), x2), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c_1, c17_3, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2


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

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c_1, c17_3, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by 
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(eq, x1) -> c(APP(eq, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(or, x1) -> c(APP(or, encArg(x1)))
   ENCODE_APP(union, x1) -> c(APP(union, encArg(x1)))
   ENCODE_APP(empty, x1) -> c(APP(empty, encArg(x1)))
   ENCODE_APP(edge, x1) -> c(APP(edge, encArg(x1)))
   ENCODE_APP(reach, x1) -> c(APP(reach, encArg(x1)))
   ENCODE_APP(if_reach_1, x1) -> c(APP(if_reach_1, encArg(x1)))
   ENCODE_APP(if_reach_2, x1) -> c(APP(if_reach_2, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(eq, x1) -> c(APP(eq, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(or, x1) -> c(APP(or, encArg(x1)))
   ENCODE_APP(union, x1) -> c(APP(union, encArg(x1)))
   ENCODE_APP(empty, x1) -> c(APP(empty, encArg(x1)))
   ENCODE_APP(edge, x1) -> c(APP(edge, encArg(x1)))
   ENCODE_APP(reach, x1) -> c(APP(reach, encArg(x1)))
   ENCODE_APP(if_reach_1, x1) -> c(APP(if_reach_1, encArg(x1)))
   ENCODE_APP(if_reach_2, x1) -> c(APP(if_reach_2, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_3, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1


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

(63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCODE_APP(empty, x1) -> c(APP(empty, encArg(x1)))
   ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(or, x1) -> c(APP(or, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(eq, x1) -> c(APP(eq, encArg(x1)))
   ENCODE_APP(if_reach_1, x1) -> c(APP(if_reach_1, encArg(x1)))
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(if_reach_2, x1) -> c(APP(if_reach_2, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(reach, x1) -> c(APP(reach, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(edge, x1) -> c(APP(edge, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(union, x1) -> c(APP(union, encArg(x1)))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_3, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c17(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by 
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(APP(eq, app(encArg(x1), encArg(x2))), ENCARG(eq), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(APP(or, app(encArg(x1), encArg(x2))), ENCARG(or), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(APP(union, app(encArg(x1), encArg(x2))), ENCARG(union), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(APP(empty, app(encArg(x1), encArg(x2))), ENCARG(empty), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(APP(edge, app(encArg(x1), encArg(x2))), ENCARG(edge), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(APP(reach, app(encArg(x1), encArg(x2))), ENCARG(reach), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(APP(if_reach_1, app(encArg(x1), encArg(x2))), ENCARG(if_reach_1), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(APP(if_reach_2, app(encArg(x1), encArg(x2))), ENCARG(if_reach_2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(APP(eq, app(encArg(x1), encArg(x2))), ENCARG(eq), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(APP(or, app(encArg(x1), encArg(x2))), ENCARG(or), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(APP(union, app(encArg(x1), encArg(x2))), ENCARG(union), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(APP(empty, app(encArg(x1), encArg(x2))), ENCARG(empty), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(APP(edge, app(encArg(x1), encArg(x2))), ENCARG(edge), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(APP(reach, app(encArg(x1), encArg(x2))), ENCARG(reach), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(APP(if_reach_1, app(encArg(x1), encArg(x2))), ENCARG(if_reach_1), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(APP(if_reach_2, app(encArg(x1), encArg(x2))), ENCARG(if_reach_2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_3, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1


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

(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 34 trailing tuple parts
----------------------------------------

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_3, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c17(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)), ENCARG(eq))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)), ENCARG(or))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)), ENCARG(union))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)), ENCARG(empty))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)), ENCARG(edge))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)), ENCARG(reach))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)), ENCARG(if_reach_1))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)), ENCARG(if_reach_2))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2))
   ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c17(APP(app(encArg(x0), encArg(x1)), app(encArg(z0), encArg(z1))), ENCARG(cons_app(x0, x1)), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(APP(app(empty, encArg(x1)), encArg(x2)), ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(APP(app(edge, encArg(x1)), encArg(x2)), ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(APP(app(reach, encArg(x1)), encArg(x2)), ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(APP(app(if_reach_1, encArg(x1)), encArg(x2)), ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(APP(app(if_reach_2, encArg(x1)), encArg(x2)), ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)), ENCARG(eq))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)), ENCARG(or))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)), ENCARG(union))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)), ENCARG(empty))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)), ENCARG(edge))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)), ENCARG(reach))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)), ENCARG(if_reach_1))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)), ENCARG(if_reach_2))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(APP(app(empty, encArg(x1)), encArg(x2)), ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(APP(app(edge, encArg(x1)), encArg(x2)), ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(APP(app(reach, encArg(x1)), encArg(x2)), ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(APP(app(if_reach_1, encArg(x1)), encArg(x2)), ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(APP(app(if_reach_2, encArg(x1)), encArg(x2)), ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, eq)) -> c17(APP(encArg(x0), eq), ENCARG(x0)) by 
   ENCARG(cons_app(eq, eq)) -> c17(APP(eq, eq), ENCARG(eq))
   ENCARG(cons_app(0, eq)) -> c17(APP(0, eq), ENCARG(0))
   ENCARG(cons_app(true, eq)) -> c17(APP(true, eq), ENCARG(true))
   ENCARG(cons_app(s, eq)) -> c17(APP(s, eq), ENCARG(s))
   ENCARG(cons_app(false, eq)) -> c17(APP(false, eq), ENCARG(false))
   ENCARG(cons_app(or, eq)) -> c17(APP(or, eq), ENCARG(or))
   ENCARG(cons_app(union, eq)) -> c17(APP(union, eq), ENCARG(union))
   ENCARG(cons_app(empty, eq)) -> c17(APP(empty, eq), ENCARG(empty))
   ENCARG(cons_app(edge, eq)) -> c17(APP(edge, eq), ENCARG(edge))
   ENCARG(cons_app(reach, eq)) -> c17(APP(reach, eq), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, eq)) -> c17(APP(if_reach_1, eq), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, eq)) -> c17(APP(if_reach_2, eq), ENCARG(if_reach_2))
   ENCARG(cons_app(map, eq)) -> c17(APP(map, eq), ENCARG(map))
   ENCARG(cons_app(nil, eq)) -> c17(APP(nil, eq), ENCARG(nil))
   ENCARG(cons_app(cons, eq)) -> c17(APP(cons, eq), ENCARG(cons))
   ENCARG(cons_app(filter, eq)) -> c17(APP(filter, eq), ENCARG(filter))
   ENCARG(cons_app(filter2, eq)) -> c17(APP(filter2, eq), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), eq)) -> c17(APP(app(encArg(z0), encArg(z1)), eq), ENCARG(cons_app(z0, z1)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, eq)) -> c17(APP(eq, eq), ENCARG(eq))
   ENCARG(cons_app(0, eq)) -> c17(APP(0, eq), ENCARG(0))
   ENCARG(cons_app(true, eq)) -> c17(APP(true, eq), ENCARG(true))
   ENCARG(cons_app(s, eq)) -> c17(APP(s, eq), ENCARG(s))
   ENCARG(cons_app(false, eq)) -> c17(APP(false, eq), ENCARG(false))
   ENCARG(cons_app(or, eq)) -> c17(APP(or, eq), ENCARG(or))
   ENCARG(cons_app(union, eq)) -> c17(APP(union, eq), ENCARG(union))
   ENCARG(cons_app(empty, eq)) -> c17(APP(empty, eq), ENCARG(empty))
   ENCARG(cons_app(edge, eq)) -> c17(APP(edge, eq), ENCARG(edge))
   ENCARG(cons_app(reach, eq)) -> c17(APP(reach, eq), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, eq)) -> c17(APP(if_reach_1, eq), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, eq)) -> c17(APP(if_reach_2, eq), ENCARG(if_reach_2))
   ENCARG(cons_app(map, eq)) -> c17(APP(map, eq), ENCARG(map))
   ENCARG(cons_app(nil, eq)) -> c17(APP(nil, eq), ENCARG(nil))
   ENCARG(cons_app(cons, eq)) -> c17(APP(cons, eq), ENCARG(cons))
   ENCARG(cons_app(filter, eq)) -> c17(APP(filter, eq), ENCARG(filter))
   ENCARG(cons_app(filter2, eq)) -> c17(APP(filter2, eq), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(false, eq)) -> c17(APP(false, eq), ENCARG(false))
   ENCARG(cons_app(map, eq)) -> c17(APP(map, eq), ENCARG(map))
   ENCARG(cons_app(if_reach_2, eq)) -> c17(APP(if_reach_2, eq), ENCARG(if_reach_2))
   ENCARG(cons_app(filter2, eq)) -> c17(APP(filter2, eq), ENCARG(filter2))
   ENCARG(cons_app(if_reach_1, eq)) -> c17(APP(if_reach_1, eq), ENCARG(if_reach_1))
   ENCARG(cons_app(edge, eq)) -> c17(APP(edge, eq), ENCARG(edge))
   ENCARG(cons_app(union, eq)) -> c17(APP(union, eq), ENCARG(union))
   ENCARG(cons_app(0, eq)) -> c17(APP(0, eq), ENCARG(0))
   ENCARG(cons_app(empty, eq)) -> c17(APP(empty, eq), ENCARG(empty))
   ENCARG(cons_app(or, eq)) -> c17(APP(or, eq), ENCARG(or))
   ENCARG(cons_app(s, eq)) -> c17(APP(s, eq), ENCARG(s))
   ENCARG(cons_app(true, eq)) -> c17(APP(true, eq), ENCARG(true))
   ENCARG(cons_app(filter, eq)) -> c17(APP(filter, eq), ENCARG(filter))
   ENCARG(cons_app(nil, eq)) -> c17(APP(nil, eq), ENCARG(nil))
   ENCARG(cons_app(reach, eq)) -> c17(APP(reach, eq), ENCARG(reach))
   ENCARG(cons_app(eq, eq)) -> c17(APP(eq, eq), ENCARG(eq))
   ENCARG(cons_app(cons, eq)) -> c17(APP(cons, eq), ENCARG(cons))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, 0)) -> c17(APP(encArg(x0), 0), ENCARG(x0)) by 
   ENCARG(cons_app(eq, 0)) -> c17(APP(eq, 0), ENCARG(eq))
   ENCARG(cons_app(0, 0)) -> c17(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(true, 0)) -> c17(APP(true, 0), ENCARG(true))
   ENCARG(cons_app(s, 0)) -> c17(APP(s, 0), ENCARG(s))
   ENCARG(cons_app(false, 0)) -> c17(APP(false, 0), ENCARG(false))
   ENCARG(cons_app(or, 0)) -> c17(APP(or, 0), ENCARG(or))
   ENCARG(cons_app(union, 0)) -> c17(APP(union, 0), ENCARG(union))
   ENCARG(cons_app(empty, 0)) -> c17(APP(empty, 0), ENCARG(empty))
   ENCARG(cons_app(edge, 0)) -> c17(APP(edge, 0), ENCARG(edge))
   ENCARG(cons_app(reach, 0)) -> c17(APP(reach, 0), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, 0)) -> c17(APP(if_reach_1, 0), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, 0)) -> c17(APP(if_reach_2, 0), ENCARG(if_reach_2))
   ENCARG(cons_app(map, 0)) -> c17(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(nil, 0)) -> c17(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(cons, 0)) -> c17(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(filter, 0)) -> c17(APP(filter, 0), ENCARG(filter))
   ENCARG(cons_app(filter2, 0)) -> c17(APP(filter2, 0), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), 0)) -> c17(APP(app(encArg(z0), encArg(z1)), 0), ENCARG(cons_app(z0, z1)))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, 0)) -> c17(APP(eq, 0), ENCARG(eq))
   ENCARG(cons_app(0, 0)) -> c17(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(true, 0)) -> c17(APP(true, 0), ENCARG(true))
   ENCARG(cons_app(s, 0)) -> c17(APP(s, 0), ENCARG(s))
   ENCARG(cons_app(false, 0)) -> c17(APP(false, 0), ENCARG(false))
   ENCARG(cons_app(or, 0)) -> c17(APP(or, 0), ENCARG(or))
   ENCARG(cons_app(union, 0)) -> c17(APP(union, 0), ENCARG(union))
   ENCARG(cons_app(empty, 0)) -> c17(APP(empty, 0), ENCARG(empty))
   ENCARG(cons_app(edge, 0)) -> c17(APP(edge, 0), ENCARG(edge))
   ENCARG(cons_app(reach, 0)) -> c17(APP(reach, 0), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, 0)) -> c17(APP(if_reach_1, 0), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, 0)) -> c17(APP(if_reach_2, 0), ENCARG(if_reach_2))
   ENCARG(cons_app(map, 0)) -> c17(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(nil, 0)) -> c17(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(cons, 0)) -> c17(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(filter, 0)) -> c17(APP(filter, 0), ENCARG(filter))
   ENCARG(cons_app(filter2, 0)) -> c17(APP(filter2, 0), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(filter2, 0)) -> c17(APP(filter2, 0), ENCARG(filter2))
   ENCARG(cons_app(map, 0)) -> c17(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(eq, 0)) -> c17(APP(eq, 0), ENCARG(eq))
   ENCARG(cons_app(empty, 0)) -> c17(APP(empty, 0), ENCARG(empty))
   ENCARG(cons_app(s, 0)) -> c17(APP(s, 0), ENCARG(s))
   ENCARG(cons_app(union, 0)) -> c17(APP(union, 0), ENCARG(union))
   ENCARG(cons_app(cons, 0)) -> c17(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(if_reach_1, 0)) -> c17(APP(if_reach_1, 0), ENCARG(if_reach_1))
   ENCARG(cons_app(0, 0)) -> c17(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(true, 0)) -> c17(APP(true, 0), ENCARG(true))
   ENCARG(cons_app(if_reach_2, 0)) -> c17(APP(if_reach_2, 0), ENCARG(if_reach_2))
   ENCARG(cons_app(filter, 0)) -> c17(APP(filter, 0), ENCARG(filter))
   ENCARG(cons_app(or, 0)) -> c17(APP(or, 0), ENCARG(or))
   ENCARG(cons_app(false, 0)) -> c17(APP(false, 0), ENCARG(false))
   ENCARG(cons_app(reach, 0)) -> c17(APP(reach, 0), ENCARG(reach))
   ENCARG(cons_app(nil, 0)) -> c17(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(edge, 0)) -> c17(APP(edge, 0), ENCARG(edge))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, true)) -> c17(APP(encArg(x0), true), ENCARG(x0)) by 
   ENCARG(cons_app(eq, true)) -> c17(APP(eq, true), ENCARG(eq))
   ENCARG(cons_app(0, true)) -> c17(APP(0, true), ENCARG(0))
   ENCARG(cons_app(true, true)) -> c17(APP(true, true), ENCARG(true))
   ENCARG(cons_app(s, true)) -> c17(APP(s, true), ENCARG(s))
   ENCARG(cons_app(false, true)) -> c17(APP(false, true), ENCARG(false))
   ENCARG(cons_app(or, true)) -> c17(APP(or, true), ENCARG(or))
   ENCARG(cons_app(union, true)) -> c17(APP(union, true), ENCARG(union))
   ENCARG(cons_app(empty, true)) -> c17(APP(empty, true), ENCARG(empty))
   ENCARG(cons_app(edge, true)) -> c17(APP(edge, true), ENCARG(edge))
   ENCARG(cons_app(reach, true)) -> c17(APP(reach, true), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, true)) -> c17(APP(if_reach_1, true), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, true)) -> c17(APP(if_reach_2, true), ENCARG(if_reach_2))
   ENCARG(cons_app(map, true)) -> c17(APP(map, true), ENCARG(map))
   ENCARG(cons_app(nil, true)) -> c17(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c17(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c17(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(filter2, true)) -> c17(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), true)) -> c17(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, true)) -> c17(APP(eq, true), ENCARG(eq))
   ENCARG(cons_app(0, true)) -> c17(APP(0, true), ENCARG(0))
   ENCARG(cons_app(true, true)) -> c17(APP(true, true), ENCARG(true))
   ENCARG(cons_app(s, true)) -> c17(APP(s, true), ENCARG(s))
   ENCARG(cons_app(false, true)) -> c17(APP(false, true), ENCARG(false))
   ENCARG(cons_app(or, true)) -> c17(APP(or, true), ENCARG(or))
   ENCARG(cons_app(union, true)) -> c17(APP(union, true), ENCARG(union))
   ENCARG(cons_app(empty, true)) -> c17(APP(empty, true), ENCARG(empty))
   ENCARG(cons_app(edge, true)) -> c17(APP(edge, true), ENCARG(edge))
   ENCARG(cons_app(reach, true)) -> c17(APP(reach, true), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, true)) -> c17(APP(if_reach_1, true), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, true)) -> c17(APP(if_reach_2, true), ENCARG(if_reach_2))
   ENCARG(cons_app(map, true)) -> c17(APP(map, true), ENCARG(map))
   ENCARG(cons_app(nil, true)) -> c17(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c17(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c17(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(filter2, true)) -> c17(APP(filter2, true), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(nil, true)) -> c17(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(false, true)) -> c17(APP(false, true), ENCARG(false))
   ENCARG(cons_app(or, true)) -> c17(APP(or, true), ENCARG(or))
   ENCARG(cons_app(filter2, true)) -> c17(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(empty, true)) -> c17(APP(empty, true), ENCARG(empty))
   ENCARG(cons_app(s, true)) -> c17(APP(s, true), ENCARG(s))
   ENCARG(cons_app(if_reach_1, true)) -> c17(APP(if_reach_1, true), ENCARG(if_reach_1))
   ENCARG(cons_app(0, true)) -> c17(APP(0, true), ENCARG(0))
   ENCARG(cons_app(eq, true)) -> c17(APP(eq, true), ENCARG(eq))
   ENCARG(cons_app(map, true)) -> c17(APP(map, true), ENCARG(map))
   ENCARG(cons_app(union, true)) -> c17(APP(union, true), ENCARG(union))
   ENCARG(cons_app(reach, true)) -> c17(APP(reach, true), ENCARG(reach))
   ENCARG(cons_app(cons, true)) -> c17(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(if_reach_2, true)) -> c17(APP(if_reach_2, true), ENCARG(if_reach_2))
   ENCARG(cons_app(edge, true)) -> c17(APP(edge, true), ENCARG(edge))
   ENCARG(cons_app(filter, true)) -> c17(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(true, true)) -> c17(APP(true, true), ENCARG(true))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, s)) -> c17(APP(encArg(x0), s), ENCARG(x0)) by 
   ENCARG(cons_app(eq, s)) -> c17(APP(eq, s), ENCARG(eq))
   ENCARG(cons_app(0, s)) -> c17(APP(0, s), ENCARG(0))
   ENCARG(cons_app(true, s)) -> c17(APP(true, s), ENCARG(true))
   ENCARG(cons_app(s, s)) -> c17(APP(s, s), ENCARG(s))
   ENCARG(cons_app(false, s)) -> c17(APP(false, s), ENCARG(false))
   ENCARG(cons_app(or, s)) -> c17(APP(or, s), ENCARG(or))
   ENCARG(cons_app(union, s)) -> c17(APP(union, s), ENCARG(union))
   ENCARG(cons_app(empty, s)) -> c17(APP(empty, s), ENCARG(empty))
   ENCARG(cons_app(edge, s)) -> c17(APP(edge, s), ENCARG(edge))
   ENCARG(cons_app(reach, s)) -> c17(APP(reach, s), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, s)) -> c17(APP(if_reach_1, s), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, s)) -> c17(APP(if_reach_2, s), ENCARG(if_reach_2))
   ENCARG(cons_app(map, s)) -> c17(APP(map, s), ENCARG(map))
   ENCARG(cons_app(nil, s)) -> c17(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(cons, s)) -> c17(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(filter, s)) -> c17(APP(filter, s), ENCARG(filter))
   ENCARG(cons_app(filter2, s)) -> c17(APP(filter2, s), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), s)) -> c17(APP(app(encArg(z0), encArg(z1)), s), ENCARG(cons_app(z0, z1)))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, s)) -> c17(APP(eq, s), ENCARG(eq))
   ENCARG(cons_app(0, s)) -> c17(APP(0, s), ENCARG(0))
   ENCARG(cons_app(true, s)) -> c17(APP(true, s), ENCARG(true))
   ENCARG(cons_app(s, s)) -> c17(APP(s, s), ENCARG(s))
   ENCARG(cons_app(false, s)) -> c17(APP(false, s), ENCARG(false))
   ENCARG(cons_app(or, s)) -> c17(APP(or, s), ENCARG(or))
   ENCARG(cons_app(union, s)) -> c17(APP(union, s), ENCARG(union))
   ENCARG(cons_app(empty, s)) -> c17(APP(empty, s), ENCARG(empty))
   ENCARG(cons_app(edge, s)) -> c17(APP(edge, s), ENCARG(edge))
   ENCARG(cons_app(reach, s)) -> c17(APP(reach, s), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, s)) -> c17(APP(if_reach_1, s), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, s)) -> c17(APP(if_reach_2, s), ENCARG(if_reach_2))
   ENCARG(cons_app(map, s)) -> c17(APP(map, s), ENCARG(map))
   ENCARG(cons_app(nil, s)) -> c17(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(cons, s)) -> c17(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(filter, s)) -> c17(APP(filter, s), ENCARG(filter))
   ENCARG(cons_app(filter2, s)) -> c17(APP(filter2, s), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(filter, s)) -> c17(APP(filter, s), ENCARG(filter))
   ENCARG(cons_app(edge, s)) -> c17(APP(edge, s), ENCARG(edge))
   ENCARG(cons_app(reach, s)) -> c17(APP(reach, s), ENCARG(reach))
   ENCARG(cons_app(nil, s)) -> c17(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(if_reach_1, s)) -> c17(APP(if_reach_1, s), ENCARG(if_reach_1))
   ENCARG(cons_app(0, s)) -> c17(APP(0, s), ENCARG(0))
   ENCARG(cons_app(or, s)) -> c17(APP(or, s), ENCARG(or))
   ENCARG(cons_app(empty, s)) -> c17(APP(empty, s), ENCARG(empty))
   ENCARG(cons_app(s, s)) -> c17(APP(s, s), ENCARG(s))
   ENCARG(cons_app(map, s)) -> c17(APP(map, s), ENCARG(map))
   ENCARG(cons_app(union, s)) -> c17(APP(union, s), ENCARG(union))
   ENCARG(cons_app(cons, s)) -> c17(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(true, s)) -> c17(APP(true, s), ENCARG(true))
   ENCARG(cons_app(if_reach_2, s)) -> c17(APP(if_reach_2, s), ENCARG(if_reach_2))
   ENCARG(cons_app(false, s)) -> c17(APP(false, s), ENCARG(false))
   ENCARG(cons_app(filter2, s)) -> c17(APP(filter2, s), ENCARG(filter2))
   ENCARG(cons_app(eq, s)) -> c17(APP(eq, s), ENCARG(eq))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, false)) -> c17(APP(encArg(x0), false), ENCARG(x0)) by 
   ENCARG(cons_app(eq, false)) -> c17(APP(eq, false), ENCARG(eq))
   ENCARG(cons_app(0, false)) -> c17(APP(0, false), ENCARG(0))
   ENCARG(cons_app(true, false)) -> c17(APP(true, false), ENCARG(true))
   ENCARG(cons_app(s, false)) -> c17(APP(s, false), ENCARG(s))
   ENCARG(cons_app(false, false)) -> c17(APP(false, false), ENCARG(false))
   ENCARG(cons_app(or, false)) -> c17(APP(or, false), ENCARG(or))
   ENCARG(cons_app(union, false)) -> c17(APP(union, false), ENCARG(union))
   ENCARG(cons_app(empty, false)) -> c17(APP(empty, false), ENCARG(empty))
   ENCARG(cons_app(edge, false)) -> c17(APP(edge, false), ENCARG(edge))
   ENCARG(cons_app(reach, false)) -> c17(APP(reach, false), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, false)) -> c17(APP(if_reach_1, false), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, false)) -> c17(APP(if_reach_2, false), ENCARG(if_reach_2))
   ENCARG(cons_app(map, false)) -> c17(APP(map, false), ENCARG(map))
   ENCARG(cons_app(nil, false)) -> c17(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c17(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(filter, false)) -> c17(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(filter2, false)) -> c17(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), false)) -> c17(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1)))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, false)) -> c17(APP(eq, false), ENCARG(eq))
   ENCARG(cons_app(0, false)) -> c17(APP(0, false), ENCARG(0))
   ENCARG(cons_app(true, false)) -> c17(APP(true, false), ENCARG(true))
   ENCARG(cons_app(s, false)) -> c17(APP(s, false), ENCARG(s))
   ENCARG(cons_app(false, false)) -> c17(APP(false, false), ENCARG(false))
   ENCARG(cons_app(or, false)) -> c17(APP(or, false), ENCARG(or))
   ENCARG(cons_app(union, false)) -> c17(APP(union, false), ENCARG(union))
   ENCARG(cons_app(empty, false)) -> c17(APP(empty, false), ENCARG(empty))
   ENCARG(cons_app(edge, false)) -> c17(APP(edge, false), ENCARG(edge))
   ENCARG(cons_app(reach, false)) -> c17(APP(reach, false), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, false)) -> c17(APP(if_reach_1, false), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, false)) -> c17(APP(if_reach_2, false), ENCARG(if_reach_2))
   ENCARG(cons_app(map, false)) -> c17(APP(map, false), ENCARG(map))
   ENCARG(cons_app(nil, false)) -> c17(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c17(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(filter, false)) -> c17(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(filter2, false)) -> c17(APP(filter2, false), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(if_reach_1, false)) -> c17(APP(if_reach_1, false), ENCARG(if_reach_1))
   ENCARG(cons_app(true, false)) -> c17(APP(true, false), ENCARG(true))
   ENCARG(cons_app(filter, false)) -> c17(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(or, false)) -> c17(APP(or, false), ENCARG(or))
   ENCARG(cons_app(eq, false)) -> c17(APP(eq, false), ENCARG(eq))
   ENCARG(cons_app(union, false)) -> c17(APP(union, false), ENCARG(union))
   ENCARG(cons_app(cons, false)) -> c17(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(if_reach_2, false)) -> c17(APP(if_reach_2, false), ENCARG(if_reach_2))
   ENCARG(cons_app(reach, false)) -> c17(APP(reach, false), ENCARG(reach))
   ENCARG(cons_app(0, false)) -> c17(APP(0, false), ENCARG(0))
   ENCARG(cons_app(filter2, false)) -> c17(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(edge, false)) -> c17(APP(edge, false), ENCARG(edge))
   ENCARG(cons_app(false, false)) -> c17(APP(false, false), ENCARG(false))
   ENCARG(cons_app(nil, false)) -> c17(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(map, false)) -> c17(APP(map, false), ENCARG(map))
   ENCARG(cons_app(empty, false)) -> c17(APP(empty, false), ENCARG(empty))
   ENCARG(cons_app(s, false)) -> c17(APP(s, false), ENCARG(s))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, or)) -> c17(APP(encArg(x0), or), ENCARG(x0)) by 
   ENCARG(cons_app(eq, or)) -> c17(APP(eq, or), ENCARG(eq))
   ENCARG(cons_app(0, or)) -> c17(APP(0, or), ENCARG(0))
   ENCARG(cons_app(true, or)) -> c17(APP(true, or), ENCARG(true))
   ENCARG(cons_app(s, or)) -> c17(APP(s, or), ENCARG(s))
   ENCARG(cons_app(false, or)) -> c17(APP(false, or), ENCARG(false))
   ENCARG(cons_app(or, or)) -> c17(APP(or, or), ENCARG(or))
   ENCARG(cons_app(union, or)) -> c17(APP(union, or), ENCARG(union))
   ENCARG(cons_app(empty, or)) -> c17(APP(empty, or), ENCARG(empty))
   ENCARG(cons_app(edge, or)) -> c17(APP(edge, or), ENCARG(edge))
   ENCARG(cons_app(reach, or)) -> c17(APP(reach, or), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, or)) -> c17(APP(if_reach_1, or), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, or)) -> c17(APP(if_reach_2, or), ENCARG(if_reach_2))
   ENCARG(cons_app(map, or)) -> c17(APP(map, or), ENCARG(map))
   ENCARG(cons_app(nil, or)) -> c17(APP(nil, or), ENCARG(nil))
   ENCARG(cons_app(cons, or)) -> c17(APP(cons, or), ENCARG(cons))
   ENCARG(cons_app(filter, or)) -> c17(APP(filter, or), ENCARG(filter))
   ENCARG(cons_app(filter2, or)) -> c17(APP(filter2, or), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), or)) -> c17(APP(app(encArg(z0), encArg(z1)), or), ENCARG(cons_app(z0, z1)))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, or)) -> c17(APP(eq, or), ENCARG(eq))
   ENCARG(cons_app(0, or)) -> c17(APP(0, or), ENCARG(0))
   ENCARG(cons_app(true, or)) -> c17(APP(true, or), ENCARG(true))
   ENCARG(cons_app(s, or)) -> c17(APP(s, or), ENCARG(s))
   ENCARG(cons_app(false, or)) -> c17(APP(false, or), ENCARG(false))
   ENCARG(cons_app(or, or)) -> c17(APP(or, or), ENCARG(or))
   ENCARG(cons_app(union, or)) -> c17(APP(union, or), ENCARG(union))
   ENCARG(cons_app(empty, or)) -> c17(APP(empty, or), ENCARG(empty))
   ENCARG(cons_app(edge, or)) -> c17(APP(edge, or), ENCARG(edge))
   ENCARG(cons_app(reach, or)) -> c17(APP(reach, or), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, or)) -> c17(APP(if_reach_1, or), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, or)) -> c17(APP(if_reach_2, or), ENCARG(if_reach_2))
   ENCARG(cons_app(map, or)) -> c17(APP(map, or), ENCARG(map))
   ENCARG(cons_app(nil, or)) -> c17(APP(nil, or), ENCARG(nil))
   ENCARG(cons_app(cons, or)) -> c17(APP(cons, or), ENCARG(cons))
   ENCARG(cons_app(filter, or)) -> c17(APP(filter, or), ENCARG(filter))
   ENCARG(cons_app(filter2, or)) -> c17(APP(filter2, or), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(or, or)) -> c17(APP(or, or), ENCARG(or))
   ENCARG(cons_app(if_reach_2, or)) -> c17(APP(if_reach_2, or), ENCARG(if_reach_2))
   ENCARG(cons_app(cons, or)) -> c17(APP(cons, or), ENCARG(cons))
   ENCARG(cons_app(nil, or)) -> c17(APP(nil, or), ENCARG(nil))
   ENCARG(cons_app(reach, or)) -> c17(APP(reach, or), ENCARG(reach))
   ENCARG(cons_app(false, or)) -> c17(APP(false, or), ENCARG(false))
   ENCARG(cons_app(union, or)) -> c17(APP(union, or), ENCARG(union))
   ENCARG(cons_app(0, or)) -> c17(APP(0, or), ENCARG(0))
   ENCARG(cons_app(map, or)) -> c17(APP(map, or), ENCARG(map))
   ENCARG(cons_app(empty, or)) -> c17(APP(empty, or), ENCARG(empty))
   ENCARG(cons_app(s, or)) -> c17(APP(s, or), ENCARG(s))
   ENCARG(cons_app(true, or)) -> c17(APP(true, or), ENCARG(true))
   ENCARG(cons_app(filter, or)) -> c17(APP(filter, or), ENCARG(filter))
   ENCARG(cons_app(if_reach_1, or)) -> c17(APP(if_reach_1, or), ENCARG(if_reach_1))
   ENCARG(cons_app(filter2, or)) -> c17(APP(filter2, or), ENCARG(filter2))
   ENCARG(cons_app(edge, or)) -> c17(APP(edge, or), ENCARG(edge))
   ENCARG(cons_app(eq, or)) -> c17(APP(eq, or), ENCARG(eq))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, union)) -> c17(APP(encArg(x0), union), ENCARG(x0)) by 
   ENCARG(cons_app(eq, union)) -> c17(APP(eq, union), ENCARG(eq))
   ENCARG(cons_app(0, union)) -> c17(APP(0, union), ENCARG(0))
   ENCARG(cons_app(true, union)) -> c17(APP(true, union), ENCARG(true))
   ENCARG(cons_app(s, union)) -> c17(APP(s, union), ENCARG(s))
   ENCARG(cons_app(false, union)) -> c17(APP(false, union), ENCARG(false))
   ENCARG(cons_app(or, union)) -> c17(APP(or, union), ENCARG(or))
   ENCARG(cons_app(union, union)) -> c17(APP(union, union), ENCARG(union))
   ENCARG(cons_app(empty, union)) -> c17(APP(empty, union), ENCARG(empty))
   ENCARG(cons_app(edge, union)) -> c17(APP(edge, union), ENCARG(edge))
   ENCARG(cons_app(reach, union)) -> c17(APP(reach, union), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, union)) -> c17(APP(if_reach_1, union), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, union)) -> c17(APP(if_reach_2, union), ENCARG(if_reach_2))
   ENCARG(cons_app(map, union)) -> c17(APP(map, union), ENCARG(map))
   ENCARG(cons_app(nil, union)) -> c17(APP(nil, union), ENCARG(nil))
   ENCARG(cons_app(cons, union)) -> c17(APP(cons, union), ENCARG(cons))
   ENCARG(cons_app(filter, union)) -> c17(APP(filter, union), ENCARG(filter))
   ENCARG(cons_app(filter2, union)) -> c17(APP(filter2, union), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), union)) -> c17(APP(app(encArg(z0), encArg(z1)), union), ENCARG(cons_app(z0, z1)))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, union)) -> c17(APP(eq, union), ENCARG(eq))
   ENCARG(cons_app(0, union)) -> c17(APP(0, union), ENCARG(0))
   ENCARG(cons_app(true, union)) -> c17(APP(true, union), ENCARG(true))
   ENCARG(cons_app(s, union)) -> c17(APP(s, union), ENCARG(s))
   ENCARG(cons_app(false, union)) -> c17(APP(false, union), ENCARG(false))
   ENCARG(cons_app(or, union)) -> c17(APP(or, union), ENCARG(or))
   ENCARG(cons_app(union, union)) -> c17(APP(union, union), ENCARG(union))
   ENCARG(cons_app(empty, union)) -> c17(APP(empty, union), ENCARG(empty))
   ENCARG(cons_app(edge, union)) -> c17(APP(edge, union), ENCARG(edge))
   ENCARG(cons_app(reach, union)) -> c17(APP(reach, union), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, union)) -> c17(APP(if_reach_1, union), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, union)) -> c17(APP(if_reach_2, union), ENCARG(if_reach_2))
   ENCARG(cons_app(map, union)) -> c17(APP(map, union), ENCARG(map))
   ENCARG(cons_app(nil, union)) -> c17(APP(nil, union), ENCARG(nil))
   ENCARG(cons_app(cons, union)) -> c17(APP(cons, union), ENCARG(cons))
   ENCARG(cons_app(filter, union)) -> c17(APP(filter, union), ENCARG(filter))
   ENCARG(cons_app(filter2, union)) -> c17(APP(filter2, union), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(true, union)) -> c17(APP(true, union), ENCARG(true))
   ENCARG(cons_app(empty, union)) -> c17(APP(empty, union), ENCARG(empty))
   ENCARG(cons_app(s, union)) -> c17(APP(s, union), ENCARG(s))
   ENCARG(cons_app(nil, union)) -> c17(APP(nil, union), ENCARG(nil))
   ENCARG(cons_app(0, union)) -> c17(APP(0, union), ENCARG(0))
   ENCARG(cons_app(map, union)) -> c17(APP(map, union), ENCARG(map))
   ENCARG(cons_app(edge, union)) -> c17(APP(edge, union), ENCARG(edge))
   ENCARG(cons_app(reach, union)) -> c17(APP(reach, union), ENCARG(reach))
   ENCARG(cons_app(eq, union)) -> c17(APP(eq, union), ENCARG(eq))
   ENCARG(cons_app(filter2, union)) -> c17(APP(filter2, union), ENCARG(filter2))
   ENCARG(cons_app(if_reach_2, union)) -> c17(APP(if_reach_2, union), ENCARG(if_reach_2))
   ENCARG(cons_app(or, union)) -> c17(APP(or, union), ENCARG(or))
   ENCARG(cons_app(cons, union)) -> c17(APP(cons, union), ENCARG(cons))
   ENCARG(cons_app(union, union)) -> c17(APP(union, union), ENCARG(union))
   ENCARG(cons_app(false, union)) -> c17(APP(false, union), ENCARG(false))
   ENCARG(cons_app(if_reach_1, union)) -> c17(APP(if_reach_1, union), ENCARG(if_reach_1))
   ENCARG(cons_app(filter, union)) -> c17(APP(filter, union), ENCARG(filter))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, empty)) -> c17(APP(encArg(x0), empty), ENCARG(x0)) by 
   ENCARG(cons_app(eq, empty)) -> c17(APP(eq, empty), ENCARG(eq))
   ENCARG(cons_app(0, empty)) -> c17(APP(0, empty), ENCARG(0))
   ENCARG(cons_app(true, empty)) -> c17(APP(true, empty), ENCARG(true))
   ENCARG(cons_app(s, empty)) -> c17(APP(s, empty), ENCARG(s))
   ENCARG(cons_app(false, empty)) -> c17(APP(false, empty), ENCARG(false))
   ENCARG(cons_app(or, empty)) -> c17(APP(or, empty), ENCARG(or))
   ENCARG(cons_app(union, empty)) -> c17(APP(union, empty), ENCARG(union))
   ENCARG(cons_app(empty, empty)) -> c17(APP(empty, empty), ENCARG(empty))
   ENCARG(cons_app(edge, empty)) -> c17(APP(edge, empty), ENCARG(edge))
   ENCARG(cons_app(reach, empty)) -> c17(APP(reach, empty), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, empty)) -> c17(APP(if_reach_1, empty), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, empty)) -> c17(APP(if_reach_2, empty), ENCARG(if_reach_2))
   ENCARG(cons_app(map, empty)) -> c17(APP(map, empty), ENCARG(map))
   ENCARG(cons_app(nil, empty)) -> c17(APP(nil, empty), ENCARG(nil))
   ENCARG(cons_app(cons, empty)) -> c17(APP(cons, empty), ENCARG(cons))
   ENCARG(cons_app(filter, empty)) -> c17(APP(filter, empty), ENCARG(filter))
   ENCARG(cons_app(filter2, empty)) -> c17(APP(filter2, empty), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), empty)) -> c17(APP(app(encArg(z0), encArg(z1)), empty), ENCARG(cons_app(z0, z1)))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, empty)) -> c17(APP(eq, empty), ENCARG(eq))
   ENCARG(cons_app(0, empty)) -> c17(APP(0, empty), ENCARG(0))
   ENCARG(cons_app(true, empty)) -> c17(APP(true, empty), ENCARG(true))
   ENCARG(cons_app(s, empty)) -> c17(APP(s, empty), ENCARG(s))
   ENCARG(cons_app(false, empty)) -> c17(APP(false, empty), ENCARG(false))
   ENCARG(cons_app(or, empty)) -> c17(APP(or, empty), ENCARG(or))
   ENCARG(cons_app(union, empty)) -> c17(APP(union, empty), ENCARG(union))
   ENCARG(cons_app(empty, empty)) -> c17(APP(empty, empty), ENCARG(empty))
   ENCARG(cons_app(edge, empty)) -> c17(APP(edge, empty), ENCARG(edge))
   ENCARG(cons_app(reach, empty)) -> c17(APP(reach, empty), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, empty)) -> c17(APP(if_reach_1, empty), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, empty)) -> c17(APP(if_reach_2, empty), ENCARG(if_reach_2))
   ENCARG(cons_app(map, empty)) -> c17(APP(map, empty), ENCARG(map))
   ENCARG(cons_app(nil, empty)) -> c17(APP(nil, empty), ENCARG(nil))
   ENCARG(cons_app(cons, empty)) -> c17(APP(cons, empty), ENCARG(cons))
   ENCARG(cons_app(filter, empty)) -> c17(APP(filter, empty), ENCARG(filter))
   ENCARG(cons_app(filter2, empty)) -> c17(APP(filter2, empty), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(if_reach_1, empty)) -> c17(APP(if_reach_1, empty), ENCARG(if_reach_1))
   ENCARG(cons_app(or, empty)) -> c17(APP(or, empty), ENCARG(or))
   ENCARG(cons_app(filter2, empty)) -> c17(APP(filter2, empty), ENCARG(filter2))
   ENCARG(cons_app(nil, empty)) -> c17(APP(nil, empty), ENCARG(nil))
   ENCARG(cons_app(filter, empty)) -> c17(APP(filter, empty), ENCARG(filter))
   ENCARG(cons_app(edge, empty)) -> c17(APP(edge, empty), ENCARG(edge))
   ENCARG(cons_app(if_reach_2, empty)) -> c17(APP(if_reach_2, empty), ENCARG(if_reach_2))
   ENCARG(cons_app(cons, empty)) -> c17(APP(cons, empty), ENCARG(cons))
   ENCARG(cons_app(0, empty)) -> c17(APP(0, empty), ENCARG(0))
   ENCARG(cons_app(map, empty)) -> c17(APP(map, empty), ENCARG(map))
   ENCARG(cons_app(reach, empty)) -> c17(APP(reach, empty), ENCARG(reach))
   ENCARG(cons_app(true, empty)) -> c17(APP(true, empty), ENCARG(true))
   ENCARG(cons_app(empty, empty)) -> c17(APP(empty, empty), ENCARG(empty))
   ENCARG(cons_app(s, empty)) -> c17(APP(s, empty), ENCARG(s))
   ENCARG(cons_app(union, empty)) -> c17(APP(union, empty), ENCARG(union))
   ENCARG(cons_app(eq, empty)) -> c17(APP(eq, empty), ENCARG(eq))
   ENCARG(cons_app(false, empty)) -> c17(APP(false, empty), ENCARG(false))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, edge)) -> c17(APP(encArg(x0), edge), ENCARG(x0)) by 
   ENCARG(cons_app(eq, edge)) -> c17(APP(eq, edge), ENCARG(eq))
   ENCARG(cons_app(0, edge)) -> c17(APP(0, edge), ENCARG(0))
   ENCARG(cons_app(true, edge)) -> c17(APP(true, edge), ENCARG(true))
   ENCARG(cons_app(s, edge)) -> c17(APP(s, edge), ENCARG(s))
   ENCARG(cons_app(false, edge)) -> c17(APP(false, edge), ENCARG(false))
   ENCARG(cons_app(or, edge)) -> c17(APP(or, edge), ENCARG(or))
   ENCARG(cons_app(union, edge)) -> c17(APP(union, edge), ENCARG(union))
   ENCARG(cons_app(empty, edge)) -> c17(APP(empty, edge), ENCARG(empty))
   ENCARG(cons_app(edge, edge)) -> c17(APP(edge, edge), ENCARG(edge))
   ENCARG(cons_app(reach, edge)) -> c17(APP(reach, edge), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, edge)) -> c17(APP(if_reach_1, edge), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, edge)) -> c17(APP(if_reach_2, edge), ENCARG(if_reach_2))
   ENCARG(cons_app(map, edge)) -> c17(APP(map, edge), ENCARG(map))
   ENCARG(cons_app(nil, edge)) -> c17(APP(nil, edge), ENCARG(nil))
   ENCARG(cons_app(cons, edge)) -> c17(APP(cons, edge), ENCARG(cons))
   ENCARG(cons_app(filter, edge)) -> c17(APP(filter, edge), ENCARG(filter))
   ENCARG(cons_app(filter2, edge)) -> c17(APP(filter2, edge), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), edge)) -> c17(APP(app(encArg(z0), encArg(z1)), edge), ENCARG(cons_app(z0, z1)))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, edge)) -> c17(APP(eq, edge), ENCARG(eq))
   ENCARG(cons_app(0, edge)) -> c17(APP(0, edge), ENCARG(0))
   ENCARG(cons_app(true, edge)) -> c17(APP(true, edge), ENCARG(true))
   ENCARG(cons_app(s, edge)) -> c17(APP(s, edge), ENCARG(s))
   ENCARG(cons_app(false, edge)) -> c17(APP(false, edge), ENCARG(false))
   ENCARG(cons_app(or, edge)) -> c17(APP(or, edge), ENCARG(or))
   ENCARG(cons_app(union, edge)) -> c17(APP(union, edge), ENCARG(union))
   ENCARG(cons_app(empty, edge)) -> c17(APP(empty, edge), ENCARG(empty))
   ENCARG(cons_app(edge, edge)) -> c17(APP(edge, edge), ENCARG(edge))
   ENCARG(cons_app(reach, edge)) -> c17(APP(reach, edge), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, edge)) -> c17(APP(if_reach_1, edge), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, edge)) -> c17(APP(if_reach_2, edge), ENCARG(if_reach_2))
   ENCARG(cons_app(map, edge)) -> c17(APP(map, edge), ENCARG(map))
   ENCARG(cons_app(nil, edge)) -> c17(APP(nil, edge), ENCARG(nil))
   ENCARG(cons_app(cons, edge)) -> c17(APP(cons, edge), ENCARG(cons))
   ENCARG(cons_app(filter, edge)) -> c17(APP(filter, edge), ENCARG(filter))
   ENCARG(cons_app(filter2, edge)) -> c17(APP(filter2, edge), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(if_reach_1, edge)) -> c17(APP(if_reach_1, edge), ENCARG(if_reach_1))
   ENCARG(cons_app(map, edge)) -> c17(APP(map, edge), ENCARG(map))
   ENCARG(cons_app(reach, edge)) -> c17(APP(reach, edge), ENCARG(reach))
   ENCARG(cons_app(true, edge)) -> c17(APP(true, edge), ENCARG(true))
   ENCARG(cons_app(nil, edge)) -> c17(APP(nil, edge), ENCARG(nil))
   ENCARG(cons_app(union, edge)) -> c17(APP(union, edge), ENCARG(union))
   ENCARG(cons_app(or, edge)) -> c17(APP(or, edge), ENCARG(or))
   ENCARG(cons_app(if_reach_2, edge)) -> c17(APP(if_reach_2, edge), ENCARG(if_reach_2))
   ENCARG(cons_app(0, edge)) -> c17(APP(0, edge), ENCARG(0))
   ENCARG(cons_app(empty, edge)) -> c17(APP(empty, edge), ENCARG(empty))
   ENCARG(cons_app(s, edge)) -> c17(APP(s, edge), ENCARG(s))
   ENCARG(cons_app(eq, edge)) -> c17(APP(eq, edge), ENCARG(eq))
   ENCARG(cons_app(cons, edge)) -> c17(APP(cons, edge), ENCARG(cons))
   ENCARG(cons_app(filter2, edge)) -> c17(APP(filter2, edge), ENCARG(filter2))
   ENCARG(cons_app(filter, edge)) -> c17(APP(filter, edge), ENCARG(filter))
   ENCARG(cons_app(false, edge)) -> c17(APP(false, edge), ENCARG(false))
   ENCARG(cons_app(edge, edge)) -> c17(APP(edge, edge), ENCARG(edge))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, reach)) -> c17(APP(encArg(x0), reach), ENCARG(x0)) by 
   ENCARG(cons_app(eq, reach)) -> c17(APP(eq, reach), ENCARG(eq))
   ENCARG(cons_app(0, reach)) -> c17(APP(0, reach), ENCARG(0))
   ENCARG(cons_app(true, reach)) -> c17(APP(true, reach), ENCARG(true))
   ENCARG(cons_app(s, reach)) -> c17(APP(s, reach), ENCARG(s))
   ENCARG(cons_app(false, reach)) -> c17(APP(false, reach), ENCARG(false))
   ENCARG(cons_app(or, reach)) -> c17(APP(or, reach), ENCARG(or))
   ENCARG(cons_app(union, reach)) -> c17(APP(union, reach), ENCARG(union))
   ENCARG(cons_app(empty, reach)) -> c17(APP(empty, reach), ENCARG(empty))
   ENCARG(cons_app(edge, reach)) -> c17(APP(edge, reach), ENCARG(edge))
   ENCARG(cons_app(reach, reach)) -> c17(APP(reach, reach), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, reach)) -> c17(APP(if_reach_1, reach), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, reach)) -> c17(APP(if_reach_2, reach), ENCARG(if_reach_2))
   ENCARG(cons_app(map, reach)) -> c17(APP(map, reach), ENCARG(map))
   ENCARG(cons_app(nil, reach)) -> c17(APP(nil, reach), ENCARG(nil))
   ENCARG(cons_app(cons, reach)) -> c17(APP(cons, reach), ENCARG(cons))
   ENCARG(cons_app(filter, reach)) -> c17(APP(filter, reach), ENCARG(filter))
   ENCARG(cons_app(filter2, reach)) -> c17(APP(filter2, reach), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), reach)) -> c17(APP(app(encArg(z0), encArg(z1)), reach), ENCARG(cons_app(z0, z1)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, reach)) -> c17(APP(eq, reach), ENCARG(eq))
   ENCARG(cons_app(0, reach)) -> c17(APP(0, reach), ENCARG(0))
   ENCARG(cons_app(true, reach)) -> c17(APP(true, reach), ENCARG(true))
   ENCARG(cons_app(s, reach)) -> c17(APP(s, reach), ENCARG(s))
   ENCARG(cons_app(false, reach)) -> c17(APP(false, reach), ENCARG(false))
   ENCARG(cons_app(or, reach)) -> c17(APP(or, reach), ENCARG(or))
   ENCARG(cons_app(union, reach)) -> c17(APP(union, reach), ENCARG(union))
   ENCARG(cons_app(empty, reach)) -> c17(APP(empty, reach), ENCARG(empty))
   ENCARG(cons_app(edge, reach)) -> c17(APP(edge, reach), ENCARG(edge))
   ENCARG(cons_app(reach, reach)) -> c17(APP(reach, reach), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, reach)) -> c17(APP(if_reach_1, reach), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, reach)) -> c17(APP(if_reach_2, reach), ENCARG(if_reach_2))
   ENCARG(cons_app(map, reach)) -> c17(APP(map, reach), ENCARG(map))
   ENCARG(cons_app(nil, reach)) -> c17(APP(nil, reach), ENCARG(nil))
   ENCARG(cons_app(cons, reach)) -> c17(APP(cons, reach), ENCARG(cons))
   ENCARG(cons_app(filter, reach)) -> c17(APP(filter, reach), ENCARG(filter))
   ENCARG(cons_app(filter2, reach)) -> c17(APP(filter2, reach), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(nil, reach)) -> c17(APP(nil, reach), ENCARG(nil))
   ENCARG(cons_app(map, reach)) -> c17(APP(map, reach), ENCARG(map))
   ENCARG(cons_app(or, reach)) -> c17(APP(or, reach), ENCARG(or))
   ENCARG(cons_app(if_reach_1, reach)) -> c17(APP(if_reach_1, reach), ENCARG(if_reach_1))
   ENCARG(cons_app(filter, reach)) -> c17(APP(filter, reach), ENCARG(filter))
   ENCARG(cons_app(edge, reach)) -> c17(APP(edge, reach), ENCARG(edge))
   ENCARG(cons_app(if_reach_2, reach)) -> c17(APP(if_reach_2, reach), ENCARG(if_reach_2))
   ENCARG(cons_app(0, reach)) -> c17(APP(0, reach), ENCARG(0))
   ENCARG(cons_app(eq, reach)) -> c17(APP(eq, reach), ENCARG(eq))
   ENCARG(cons_app(union, reach)) -> c17(APP(union, reach), ENCARG(union))
   ENCARG(cons_app(filter2, reach)) -> c17(APP(filter2, reach), ENCARG(filter2))
   ENCARG(cons_app(empty, reach)) -> c17(APP(empty, reach), ENCARG(empty))
   ENCARG(cons_app(s, reach)) -> c17(APP(s, reach), ENCARG(s))
   ENCARG(cons_app(cons, reach)) -> c17(APP(cons, reach), ENCARG(cons))
   ENCARG(cons_app(true, reach)) -> c17(APP(true, reach), ENCARG(true))
   ENCARG(cons_app(reach, reach)) -> c17(APP(reach, reach), ENCARG(reach))
   ENCARG(cons_app(false, reach)) -> c17(APP(false, reach), ENCARG(false))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, if_reach_1)) -> c17(APP(encArg(x0), if_reach_1), ENCARG(x0)) by 
   ENCARG(cons_app(eq, if_reach_1)) -> c17(APP(eq, if_reach_1), ENCARG(eq))
   ENCARG(cons_app(0, if_reach_1)) -> c17(APP(0, if_reach_1), ENCARG(0))
   ENCARG(cons_app(true, if_reach_1)) -> c17(APP(true, if_reach_1), ENCARG(true))
   ENCARG(cons_app(s, if_reach_1)) -> c17(APP(s, if_reach_1), ENCARG(s))
   ENCARG(cons_app(false, if_reach_1)) -> c17(APP(false, if_reach_1), ENCARG(false))
   ENCARG(cons_app(or, if_reach_1)) -> c17(APP(or, if_reach_1), ENCARG(or))
   ENCARG(cons_app(union, if_reach_1)) -> c17(APP(union, if_reach_1), ENCARG(union))
   ENCARG(cons_app(empty, if_reach_1)) -> c17(APP(empty, if_reach_1), ENCARG(empty))
   ENCARG(cons_app(edge, if_reach_1)) -> c17(APP(edge, if_reach_1), ENCARG(edge))
   ENCARG(cons_app(reach, if_reach_1)) -> c17(APP(reach, if_reach_1), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, if_reach_1)) -> c17(APP(if_reach_1, if_reach_1), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, if_reach_1)) -> c17(APP(if_reach_2, if_reach_1), ENCARG(if_reach_2))
   ENCARG(cons_app(map, if_reach_1)) -> c17(APP(map, if_reach_1), ENCARG(map))
   ENCARG(cons_app(nil, if_reach_1)) -> c17(APP(nil, if_reach_1), ENCARG(nil))
   ENCARG(cons_app(cons, if_reach_1)) -> c17(APP(cons, if_reach_1), ENCARG(cons))
   ENCARG(cons_app(filter, if_reach_1)) -> c17(APP(filter, if_reach_1), ENCARG(filter))
   ENCARG(cons_app(filter2, if_reach_1)) -> c17(APP(filter2, if_reach_1), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), if_reach_1)) -> c17(APP(app(encArg(z0), encArg(z1)), if_reach_1), ENCARG(cons_app(z0, z1)))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, if_reach_1)) -> c17(APP(eq, if_reach_1), ENCARG(eq))
   ENCARG(cons_app(0, if_reach_1)) -> c17(APP(0, if_reach_1), ENCARG(0))
   ENCARG(cons_app(true, if_reach_1)) -> c17(APP(true, if_reach_1), ENCARG(true))
   ENCARG(cons_app(s, if_reach_1)) -> c17(APP(s, if_reach_1), ENCARG(s))
   ENCARG(cons_app(false, if_reach_1)) -> c17(APP(false, if_reach_1), ENCARG(false))
   ENCARG(cons_app(or, if_reach_1)) -> c17(APP(or, if_reach_1), ENCARG(or))
   ENCARG(cons_app(union, if_reach_1)) -> c17(APP(union, if_reach_1), ENCARG(union))
   ENCARG(cons_app(empty, if_reach_1)) -> c17(APP(empty, if_reach_1), ENCARG(empty))
   ENCARG(cons_app(edge, if_reach_1)) -> c17(APP(edge, if_reach_1), ENCARG(edge))
   ENCARG(cons_app(reach, if_reach_1)) -> c17(APP(reach, if_reach_1), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, if_reach_1)) -> c17(APP(if_reach_1, if_reach_1), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, if_reach_1)) -> c17(APP(if_reach_2, if_reach_1), ENCARG(if_reach_2))
   ENCARG(cons_app(map, if_reach_1)) -> c17(APP(map, if_reach_1), ENCARG(map))
   ENCARG(cons_app(nil, if_reach_1)) -> c17(APP(nil, if_reach_1), ENCARG(nil))
   ENCARG(cons_app(cons, if_reach_1)) -> c17(APP(cons, if_reach_1), ENCARG(cons))
   ENCARG(cons_app(filter, if_reach_1)) -> c17(APP(filter, if_reach_1), ENCARG(filter))
   ENCARG(cons_app(filter2, if_reach_1)) -> c17(APP(filter2, if_reach_1), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(or, if_reach_1)) -> c17(APP(or, if_reach_1), ENCARG(or))
   ENCARG(cons_app(if_reach_2, if_reach_1)) -> c17(APP(if_reach_2, if_reach_1), ENCARG(if_reach_2))
   ENCARG(cons_app(reach, if_reach_1)) -> c17(APP(reach, if_reach_1), ENCARG(reach))
   ENCARG(cons_app(filter2, if_reach_1)) -> c17(APP(filter2, if_reach_1), ENCARG(filter2))
   ENCARG(cons_app(cons, if_reach_1)) -> c17(APP(cons, if_reach_1), ENCARG(cons))
   ENCARG(cons_app(nil, if_reach_1)) -> c17(APP(nil, if_reach_1), ENCARG(nil))
   ENCARG(cons_app(union, if_reach_1)) -> c17(APP(union, if_reach_1), ENCARG(union))
   ENCARG(cons_app(eq, if_reach_1)) -> c17(APP(eq, if_reach_1), ENCARG(eq))
   ENCARG(cons_app(map, if_reach_1)) -> c17(APP(map, if_reach_1), ENCARG(map))
   ENCARG(cons_app(empty, if_reach_1)) -> c17(APP(empty, if_reach_1), ENCARG(empty))
   ENCARG(cons_app(s, if_reach_1)) -> c17(APP(s, if_reach_1), ENCARG(s))
   ENCARG(cons_app(0, if_reach_1)) -> c17(APP(0, if_reach_1), ENCARG(0))
   ENCARG(cons_app(filter, if_reach_1)) -> c17(APP(filter, if_reach_1), ENCARG(filter))
   ENCARG(cons_app(true, if_reach_1)) -> c17(APP(true, if_reach_1), ENCARG(true))
   ENCARG(cons_app(if_reach_1, if_reach_1)) -> c17(APP(if_reach_1, if_reach_1), ENCARG(if_reach_1))
   ENCARG(cons_app(false, if_reach_1)) -> c17(APP(false, if_reach_1), ENCARG(false))
   ENCARG(cons_app(edge, if_reach_1)) -> c17(APP(edge, if_reach_1), ENCARG(edge))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, if_reach_2)) -> c17(APP(encArg(x0), if_reach_2), ENCARG(x0)) by 
   ENCARG(cons_app(eq, if_reach_2)) -> c17(APP(eq, if_reach_2), ENCARG(eq))
   ENCARG(cons_app(0, if_reach_2)) -> c17(APP(0, if_reach_2), ENCARG(0))
   ENCARG(cons_app(true, if_reach_2)) -> c17(APP(true, if_reach_2), ENCARG(true))
   ENCARG(cons_app(s, if_reach_2)) -> c17(APP(s, if_reach_2), ENCARG(s))
   ENCARG(cons_app(false, if_reach_2)) -> c17(APP(false, if_reach_2), ENCARG(false))
   ENCARG(cons_app(or, if_reach_2)) -> c17(APP(or, if_reach_2), ENCARG(or))
   ENCARG(cons_app(union, if_reach_2)) -> c17(APP(union, if_reach_2), ENCARG(union))
   ENCARG(cons_app(empty, if_reach_2)) -> c17(APP(empty, if_reach_2), ENCARG(empty))
   ENCARG(cons_app(edge, if_reach_2)) -> c17(APP(edge, if_reach_2), ENCARG(edge))
   ENCARG(cons_app(reach, if_reach_2)) -> c17(APP(reach, if_reach_2), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, if_reach_2)) -> c17(APP(if_reach_1, if_reach_2), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, if_reach_2)) -> c17(APP(if_reach_2, if_reach_2), ENCARG(if_reach_2))
   ENCARG(cons_app(map, if_reach_2)) -> c17(APP(map, if_reach_2), ENCARG(map))
   ENCARG(cons_app(nil, if_reach_2)) -> c17(APP(nil, if_reach_2), ENCARG(nil))
   ENCARG(cons_app(cons, if_reach_2)) -> c17(APP(cons, if_reach_2), ENCARG(cons))
   ENCARG(cons_app(filter, if_reach_2)) -> c17(APP(filter, if_reach_2), ENCARG(filter))
   ENCARG(cons_app(filter2, if_reach_2)) -> c17(APP(filter2, if_reach_2), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), if_reach_2)) -> c17(APP(app(encArg(z0), encArg(z1)), if_reach_2), ENCARG(cons_app(z0, z1)))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, if_reach_2)) -> c17(APP(eq, if_reach_2), ENCARG(eq))
   ENCARG(cons_app(0, if_reach_2)) -> c17(APP(0, if_reach_2), ENCARG(0))
   ENCARG(cons_app(true, if_reach_2)) -> c17(APP(true, if_reach_2), ENCARG(true))
   ENCARG(cons_app(s, if_reach_2)) -> c17(APP(s, if_reach_2), ENCARG(s))
   ENCARG(cons_app(false, if_reach_2)) -> c17(APP(false, if_reach_2), ENCARG(false))
   ENCARG(cons_app(or, if_reach_2)) -> c17(APP(or, if_reach_2), ENCARG(or))
   ENCARG(cons_app(union, if_reach_2)) -> c17(APP(union, if_reach_2), ENCARG(union))
   ENCARG(cons_app(empty, if_reach_2)) -> c17(APP(empty, if_reach_2), ENCARG(empty))
   ENCARG(cons_app(edge, if_reach_2)) -> c17(APP(edge, if_reach_2), ENCARG(edge))
   ENCARG(cons_app(reach, if_reach_2)) -> c17(APP(reach, if_reach_2), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, if_reach_2)) -> c17(APP(if_reach_1, if_reach_2), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, if_reach_2)) -> c17(APP(if_reach_2, if_reach_2), ENCARG(if_reach_2))
   ENCARG(cons_app(map, if_reach_2)) -> c17(APP(map, if_reach_2), ENCARG(map))
   ENCARG(cons_app(nil, if_reach_2)) -> c17(APP(nil, if_reach_2), ENCARG(nil))
   ENCARG(cons_app(cons, if_reach_2)) -> c17(APP(cons, if_reach_2), ENCARG(cons))
   ENCARG(cons_app(filter, if_reach_2)) -> c17(APP(filter, if_reach_2), ENCARG(filter))
   ENCARG(cons_app(filter2, if_reach_2)) -> c17(APP(filter2, if_reach_2), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(if_reach_2, if_reach_2)) -> c17(APP(if_reach_2, if_reach_2), ENCARG(if_reach_2))
   ENCARG(cons_app(edge, if_reach_2)) -> c17(APP(edge, if_reach_2), ENCARG(edge))
   ENCARG(cons_app(false, if_reach_2)) -> c17(APP(false, if_reach_2), ENCARG(false))
   ENCARG(cons_app(true, if_reach_2)) -> c17(APP(true, if_reach_2), ENCARG(true))
   ENCARG(cons_app(map, if_reach_2)) -> c17(APP(map, if_reach_2), ENCARG(map))
   ENCARG(cons_app(if_reach_1, if_reach_2)) -> c17(APP(if_reach_1, if_reach_2), ENCARG(if_reach_1))
   ENCARG(cons_app(cons, if_reach_2)) -> c17(APP(cons, if_reach_2), ENCARG(cons))
   ENCARG(cons_app(eq, if_reach_2)) -> c17(APP(eq, if_reach_2), ENCARG(eq))
   ENCARG(cons_app(or, if_reach_2)) -> c17(APP(or, if_reach_2), ENCARG(or))
   ENCARG(cons_app(filter2, if_reach_2)) -> c17(APP(filter2, if_reach_2), ENCARG(filter2))
   ENCARG(cons_app(empty, if_reach_2)) -> c17(APP(empty, if_reach_2), ENCARG(empty))
   ENCARG(cons_app(s, if_reach_2)) -> c17(APP(s, if_reach_2), ENCARG(s))
   ENCARG(cons_app(0, if_reach_2)) -> c17(APP(0, if_reach_2), ENCARG(0))
   ENCARG(cons_app(filter, if_reach_2)) -> c17(APP(filter, if_reach_2), ENCARG(filter))
   ENCARG(cons_app(nil, if_reach_2)) -> c17(APP(nil, if_reach_2), ENCARG(nil))
   ENCARG(cons_app(reach, if_reach_2)) -> c17(APP(reach, if_reach_2), ENCARG(reach))
   ENCARG(cons_app(union, if_reach_2)) -> c17(APP(union, if_reach_2), ENCARG(union))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, map)) -> c17(APP(encArg(x0), map), ENCARG(x0)) by 
   ENCARG(cons_app(eq, map)) -> c17(APP(eq, map), ENCARG(eq))
   ENCARG(cons_app(0, map)) -> c17(APP(0, map), ENCARG(0))
   ENCARG(cons_app(true, map)) -> c17(APP(true, map), ENCARG(true))
   ENCARG(cons_app(s, map)) -> c17(APP(s, map), ENCARG(s))
   ENCARG(cons_app(false, map)) -> c17(APP(false, map), ENCARG(false))
   ENCARG(cons_app(or, map)) -> c17(APP(or, map), ENCARG(or))
   ENCARG(cons_app(union, map)) -> c17(APP(union, map), ENCARG(union))
   ENCARG(cons_app(empty, map)) -> c17(APP(empty, map), ENCARG(empty))
   ENCARG(cons_app(edge, map)) -> c17(APP(edge, map), ENCARG(edge))
   ENCARG(cons_app(reach, map)) -> c17(APP(reach, map), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, map)) -> c17(APP(if_reach_1, map), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, map)) -> c17(APP(if_reach_2, map), ENCARG(if_reach_2))
   ENCARG(cons_app(map, map)) -> c17(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c17(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c17(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(filter, map)) -> c17(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(filter2, map)) -> c17(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), map)) -> c17(APP(app(encArg(z0), encArg(z1)), map), ENCARG(cons_app(z0, z1)))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, map)) -> c17(APP(eq, map), ENCARG(eq))
   ENCARG(cons_app(0, map)) -> c17(APP(0, map), ENCARG(0))
   ENCARG(cons_app(true, map)) -> c17(APP(true, map), ENCARG(true))
   ENCARG(cons_app(s, map)) -> c17(APP(s, map), ENCARG(s))
   ENCARG(cons_app(false, map)) -> c17(APP(false, map), ENCARG(false))
   ENCARG(cons_app(or, map)) -> c17(APP(or, map), ENCARG(or))
   ENCARG(cons_app(union, map)) -> c17(APP(union, map), ENCARG(union))
   ENCARG(cons_app(empty, map)) -> c17(APP(empty, map), ENCARG(empty))
   ENCARG(cons_app(edge, map)) -> c17(APP(edge, map), ENCARG(edge))
   ENCARG(cons_app(reach, map)) -> c17(APP(reach, map), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, map)) -> c17(APP(if_reach_1, map), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, map)) -> c17(APP(if_reach_2, map), ENCARG(if_reach_2))
   ENCARG(cons_app(map, map)) -> c17(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c17(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c17(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(filter, map)) -> c17(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(filter2, map)) -> c17(APP(filter2, map), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(filter, map)) -> c17(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(map, map)) -> c17(APP(map, map), ENCARG(map))
   ENCARG(cons_app(reach, map)) -> c17(APP(reach, map), ENCARG(reach))
   ENCARG(cons_app(cons, map)) -> c17(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(false, map)) -> c17(APP(false, map), ENCARG(false))
   ENCARG(cons_app(eq, map)) -> c17(APP(eq, map), ENCARG(eq))
   ENCARG(cons_app(0, map)) -> c17(APP(0, map), ENCARG(0))
   ENCARG(cons_app(or, map)) -> c17(APP(or, map), ENCARG(or))
   ENCARG(cons_app(empty, map)) -> c17(APP(empty, map), ENCARG(empty))
   ENCARG(cons_app(s, map)) -> c17(APP(s, map), ENCARG(s))
   ENCARG(cons_app(if_reach_2, map)) -> c17(APP(if_reach_2, map), ENCARG(if_reach_2))
   ENCARG(cons_app(true, map)) -> c17(APP(true, map), ENCARG(true))
   ENCARG(cons_app(nil, map)) -> c17(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(union, map)) -> c17(APP(union, map), ENCARG(union))
   ENCARG(cons_app(if_reach_1, map)) -> c17(APP(if_reach_1, map), ENCARG(if_reach_1))
   ENCARG(cons_app(filter2, map)) -> c17(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(edge, map)) -> c17(APP(edge, map), ENCARG(edge))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c17(APP(encArg(x0), nil), ENCARG(x0)) by 
   ENCARG(cons_app(eq, nil)) -> c17(APP(eq, nil), ENCARG(eq))
   ENCARG(cons_app(0, nil)) -> c17(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(true, nil)) -> c17(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(s, nil)) -> c17(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(false, nil)) -> c17(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(or, nil)) -> c17(APP(or, nil), ENCARG(or))
   ENCARG(cons_app(union, nil)) -> c17(APP(union, nil), ENCARG(union))
   ENCARG(cons_app(empty, nil)) -> c17(APP(empty, nil), ENCARG(empty))
   ENCARG(cons_app(edge, nil)) -> c17(APP(edge, nil), ENCARG(edge))
   ENCARG(cons_app(reach, nil)) -> c17(APP(reach, nil), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, nil)) -> c17(APP(if_reach_1, nil), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, nil)) -> c17(APP(if_reach_2, nil), ENCARG(if_reach_2))
   ENCARG(cons_app(map, nil)) -> c17(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c17(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c17(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(filter, nil)) -> c17(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(filter2, nil)) -> c17(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), nil)) -> c17(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1)))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, nil)) -> c17(APP(eq, nil), ENCARG(eq))
   ENCARG(cons_app(0, nil)) -> c17(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(true, nil)) -> c17(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(s, nil)) -> c17(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(false, nil)) -> c17(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(or, nil)) -> c17(APP(or, nil), ENCARG(or))
   ENCARG(cons_app(union, nil)) -> c17(APP(union, nil), ENCARG(union))
   ENCARG(cons_app(empty, nil)) -> c17(APP(empty, nil), ENCARG(empty))
   ENCARG(cons_app(edge, nil)) -> c17(APP(edge, nil), ENCARG(edge))
   ENCARG(cons_app(reach, nil)) -> c17(APP(reach, nil), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, nil)) -> c17(APP(if_reach_1, nil), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, nil)) -> c17(APP(if_reach_2, nil), ENCARG(if_reach_2))
   ENCARG(cons_app(map, nil)) -> c17(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c17(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c17(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(filter, nil)) -> c17(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(filter2, nil)) -> c17(APP(filter2, nil), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(filter, nil)) -> c17(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(reach, nil)) -> c17(APP(reach, nil), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, nil)) -> c17(APP(if_reach_1, nil), ENCARG(if_reach_1))
   ENCARG(cons_app(nil, nil)) -> c17(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(empty, nil)) -> c17(APP(empty, nil), ENCARG(empty))
   ENCARG(cons_app(s, nil)) -> c17(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(0, nil)) -> c17(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(filter2, nil)) -> c17(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(edge, nil)) -> c17(APP(edge, nil), ENCARG(edge))
   ENCARG(cons_app(or, nil)) -> c17(APP(or, nil), ENCARG(or))
   ENCARG(cons_app(map, nil)) -> c17(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(false, nil)) -> c17(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(eq, nil)) -> c17(APP(eq, nil), ENCARG(eq))
   ENCARG(cons_app(union, nil)) -> c17(APP(union, nil), ENCARG(union))
   ENCARG(cons_app(cons, nil)) -> c17(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(if_reach_2, nil)) -> c17(APP(if_reach_2, nil), ENCARG(if_reach_2))
   ENCARG(cons_app(true, nil)) -> c17(APP(true, nil), ENCARG(true))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c17(APP(encArg(x0), cons), ENCARG(x0)) by 
   ENCARG(cons_app(eq, cons)) -> c17(APP(eq, cons), ENCARG(eq))
   ENCARG(cons_app(0, cons)) -> c17(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(true, cons)) -> c17(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(s, cons)) -> c17(APP(s, cons), ENCARG(s))
   ENCARG(cons_app(false, cons)) -> c17(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(or, cons)) -> c17(APP(or, cons), ENCARG(or))
   ENCARG(cons_app(union, cons)) -> c17(APP(union, cons), ENCARG(union))
   ENCARG(cons_app(empty, cons)) -> c17(APP(empty, cons), ENCARG(empty))
   ENCARG(cons_app(edge, cons)) -> c17(APP(edge, cons), ENCARG(edge))
   ENCARG(cons_app(reach, cons)) -> c17(APP(reach, cons), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, cons)) -> c17(APP(if_reach_1, cons), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, cons)) -> c17(APP(if_reach_2, cons), ENCARG(if_reach_2))
   ENCARG(cons_app(map, cons)) -> c17(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c17(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c17(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(filter, cons)) -> c17(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(filter2, cons)) -> c17(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), cons)) -> c17(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1)))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, cons)) -> c17(APP(eq, cons), ENCARG(eq))
   ENCARG(cons_app(0, cons)) -> c17(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(true, cons)) -> c17(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(s, cons)) -> c17(APP(s, cons), ENCARG(s))
   ENCARG(cons_app(false, cons)) -> c17(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(or, cons)) -> c17(APP(or, cons), ENCARG(or))
   ENCARG(cons_app(union, cons)) -> c17(APP(union, cons), ENCARG(union))
   ENCARG(cons_app(empty, cons)) -> c17(APP(empty, cons), ENCARG(empty))
   ENCARG(cons_app(edge, cons)) -> c17(APP(edge, cons), ENCARG(edge))
   ENCARG(cons_app(reach, cons)) -> c17(APP(reach, cons), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, cons)) -> c17(APP(if_reach_1, cons), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, cons)) -> c17(APP(if_reach_2, cons), ENCARG(if_reach_2))
   ENCARG(cons_app(map, cons)) -> c17(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c17(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c17(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(filter, cons)) -> c17(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(filter2, cons)) -> c17(APP(filter2, cons), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(map, cons)) -> c17(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(false, cons)) -> c17(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(filter, cons)) -> c17(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(cons, cons)) -> c17(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(eq, cons)) -> c17(APP(eq, cons), ENCARG(eq))
   ENCARG(cons_app(empty, cons)) -> c17(APP(empty, cons), ENCARG(empty))
   ENCARG(cons_app(s, cons)) -> c17(APP(s, cons), ENCARG(s))
   ENCARG(cons_app(union, cons)) -> c17(APP(union, cons), ENCARG(union))
   ENCARG(cons_app(if_reach_2, cons)) -> c17(APP(if_reach_2, cons), ENCARG(if_reach_2))
   ENCARG(cons_app(if_reach_1, cons)) -> c17(APP(if_reach_1, cons), ENCARG(if_reach_1))
   ENCARG(cons_app(edge, cons)) -> c17(APP(edge, cons), ENCARG(edge))
   ENCARG(cons_app(or, cons)) -> c17(APP(or, cons), ENCARG(or))
   ENCARG(cons_app(0, cons)) -> c17(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(true, cons)) -> c17(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(filter2, cons)) -> c17(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(reach, cons)) -> c17(APP(reach, cons), ENCARG(reach))
   ENCARG(cons_app(nil, cons)) -> c17(APP(nil, cons), ENCARG(nil))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c17(APP(encArg(x0), filter), ENCARG(x0)) by 
   ENCARG(cons_app(eq, filter)) -> c17(APP(eq, filter), ENCARG(eq))
   ENCARG(cons_app(0, filter)) -> c17(APP(0, filter), ENCARG(0))
   ENCARG(cons_app(true, filter)) -> c17(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(s, filter)) -> c17(APP(s, filter), ENCARG(s))
   ENCARG(cons_app(false, filter)) -> c17(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(or, filter)) -> c17(APP(or, filter), ENCARG(or))
   ENCARG(cons_app(union, filter)) -> c17(APP(union, filter), ENCARG(union))
   ENCARG(cons_app(empty, filter)) -> c17(APP(empty, filter), ENCARG(empty))
   ENCARG(cons_app(edge, filter)) -> c17(APP(edge, filter), ENCARG(edge))
   ENCARG(cons_app(reach, filter)) -> c17(APP(reach, filter), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, filter)) -> c17(APP(if_reach_1, filter), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, filter)) -> c17(APP(if_reach_2, filter), ENCARG(if_reach_2))
   ENCARG(cons_app(map, filter)) -> c17(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(nil, filter)) -> c17(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons, filter)) -> c17(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c17(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(filter2, filter)) -> c17(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), filter)) -> c17(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1)))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, filter)) -> c17(APP(eq, filter), ENCARG(eq))
   ENCARG(cons_app(0, filter)) -> c17(APP(0, filter), ENCARG(0))
   ENCARG(cons_app(true, filter)) -> c17(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(s, filter)) -> c17(APP(s, filter), ENCARG(s))
   ENCARG(cons_app(false, filter)) -> c17(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(or, filter)) -> c17(APP(or, filter), ENCARG(or))
   ENCARG(cons_app(union, filter)) -> c17(APP(union, filter), ENCARG(union))
   ENCARG(cons_app(empty, filter)) -> c17(APP(empty, filter), ENCARG(empty))
   ENCARG(cons_app(edge, filter)) -> c17(APP(edge, filter), ENCARG(edge))
   ENCARG(cons_app(reach, filter)) -> c17(APP(reach, filter), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, filter)) -> c17(APP(if_reach_1, filter), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, filter)) -> c17(APP(if_reach_2, filter), ENCARG(if_reach_2))
   ENCARG(cons_app(map, filter)) -> c17(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(nil, filter)) -> c17(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons, filter)) -> c17(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c17(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(filter2, filter)) -> c17(APP(filter2, filter), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(if_reach_2, filter)) -> c17(APP(if_reach_2, filter), ENCARG(if_reach_2))
   ENCARG(cons_app(true, filter)) -> c17(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(or, filter)) -> c17(APP(or, filter), ENCARG(or))
   ENCARG(cons_app(false, filter)) -> c17(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(eq, filter)) -> c17(APP(eq, filter), ENCARG(eq))
   ENCARG(cons_app(filter2, filter)) -> c17(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(if_reach_1, filter)) -> c17(APP(if_reach_1, filter), ENCARG(if_reach_1))
   ENCARG(cons_app(cons, filter)) -> c17(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c17(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(edge, filter)) -> c17(APP(edge, filter), ENCARG(edge))
   ENCARG(cons_app(nil, filter)) -> c17(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(union, filter)) -> c17(APP(union, filter), ENCARG(union))
   ENCARG(cons_app(empty, filter)) -> c17(APP(empty, filter), ENCARG(empty))
   ENCARG(cons_app(s, filter)) -> c17(APP(s, filter), ENCARG(s))
   ENCARG(cons_app(map, filter)) -> c17(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(reach, filter)) -> c17(APP(reach, filter), ENCARG(reach))
   ENCARG(cons_app(0, filter)) -> c17(APP(0, filter), ENCARG(0))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_2, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3


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

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter2)) -> c17(APP(encArg(x0), filter2), ENCARG(x0)) by 
   ENCARG(cons_app(eq, filter2)) -> c17(APP(eq, filter2), ENCARG(eq))
   ENCARG(cons_app(0, filter2)) -> c17(APP(0, filter2), ENCARG(0))
   ENCARG(cons_app(true, filter2)) -> c17(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(s, filter2)) -> c17(APP(s, filter2), ENCARG(s))
   ENCARG(cons_app(false, filter2)) -> c17(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(or, filter2)) -> c17(APP(or, filter2), ENCARG(or))
   ENCARG(cons_app(union, filter2)) -> c17(APP(union, filter2), ENCARG(union))
   ENCARG(cons_app(empty, filter2)) -> c17(APP(empty, filter2), ENCARG(empty))
   ENCARG(cons_app(edge, filter2)) -> c17(APP(edge, filter2), ENCARG(edge))
   ENCARG(cons_app(reach, filter2)) -> c17(APP(reach, filter2), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, filter2)) -> c17(APP(if_reach_1, filter2), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, filter2)) -> c17(APP(if_reach_2, filter2), ENCARG(if_reach_2))
   ENCARG(cons_app(map, filter2)) -> c17(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(nil, filter2)) -> c17(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(cons, filter2)) -> c17(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(filter, filter2)) -> c17(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(filter2, filter2)) -> c17(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(cons_app(z0, z1), filter2)) -> c17(APP(app(encArg(z0), encArg(z1)), filter2), ENCARG(cons_app(z0, z1)))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(eq, filter2)) -> c17(APP(eq, filter2), ENCARG(eq))
   ENCARG(cons_app(0, filter2)) -> c17(APP(0, filter2), ENCARG(0))
   ENCARG(cons_app(true, filter2)) -> c17(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(s, filter2)) -> c17(APP(s, filter2), ENCARG(s))
   ENCARG(cons_app(false, filter2)) -> c17(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(or, filter2)) -> c17(APP(or, filter2), ENCARG(or))
   ENCARG(cons_app(union, filter2)) -> c17(APP(union, filter2), ENCARG(union))
   ENCARG(cons_app(empty, filter2)) -> c17(APP(empty, filter2), ENCARG(empty))
   ENCARG(cons_app(edge, filter2)) -> c17(APP(edge, filter2), ENCARG(edge))
   ENCARG(cons_app(reach, filter2)) -> c17(APP(reach, filter2), ENCARG(reach))
   ENCARG(cons_app(if_reach_1, filter2)) -> c17(APP(if_reach_1, filter2), ENCARG(if_reach_1))
   ENCARG(cons_app(if_reach_2, filter2)) -> c17(APP(if_reach_2, filter2), ENCARG(if_reach_2))
   ENCARG(cons_app(map, filter2)) -> c17(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(nil, filter2)) -> c17(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(cons, filter2)) -> c17(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(filter, filter2)) -> c17(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(filter2, filter2)) -> c17(APP(filter2, filter2), ENCARG(filter2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3, c17_2


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

(139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   ENCARG(cons_app(union, filter2)) -> c17(APP(union, filter2), ENCARG(union))
   ENCARG(cons_app(eq, filter2)) -> c17(APP(eq, filter2), ENCARG(eq))
   ENCARG(cons_app(map, filter2)) -> c17(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(if_reach_1, filter2)) -> c17(APP(if_reach_1, filter2), ENCARG(if_reach_1))
   ENCARG(cons_app(false, filter2)) -> c17(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(true, filter2)) -> c17(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(or, filter2)) -> c17(APP(or, filter2), ENCARG(or))
   ENCARG(cons_app(filter, filter2)) -> c17(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(nil, filter2)) -> c17(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(if_reach_2, filter2)) -> c17(APP(if_reach_2, filter2), ENCARG(if_reach_2))
   ENCARG(cons_app(reach, filter2)) -> c17(APP(reach, filter2), ENCARG(reach))
   ENCARG(cons_app(filter2, filter2)) -> c17(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(cons, filter2)) -> c17(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(0, filter2)) -> c17(APP(0, filter2), ENCARG(0))
   ENCARG(cons_app(edge, filter2)) -> c17(APP(edge, filter2), ENCARG(edge))
   ENCARG(cons_app(empty, filter2)) -> c17(APP(empty, filter2), ENCARG(empty))
   ENCARG(cons_app(s, filter2)) -> c17(APP(s, filter2), ENCARG(s))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3, c17_2


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, z0)), x1), app(app(app(edge, app(s, z1)), x3), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1))) by 
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3, c17_2, c45_1


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, z0)), app(app(app(edge, x2), app(s, z1)), x4)), x5), APP(app(eq, app(s, z0)), app(s, z1))) by 
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, x1)), app(app(app(edge, x2), app(s, x3)), x4)), x5) -> c46(APP(app(eq, app(s, x1)), app(s, x3)))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, x1)), app(app(app(edge, x2), app(s, x3)), x4)), x5) -> c46(APP(app(eq, app(s, x1)), app(s, x3)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, x1)), app(app(app(edge, x2), app(s, x3)), x4)), x5) -> c46(APP(app(eq, app(s, x1)), app(s, x3)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3, c17_2, c45_1, c46_1


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

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, x1)), app(app(app(edge, x2), app(s, x3)), x4)), x5) -> c46(APP(app(eq, app(s, x1)), app(s, x3)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c2(APP(app(app(app(app(if_reach_2, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c2(APP(app(eq, app(s, 0)), app(s, 0)))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, x1)), app(app(app(edge, x2), app(s, x3)), x4)), x5) -> c46(APP(app(eq, app(s, x1)), app(s, x3)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c2(APP(app(app(app(app(if_reach_2, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c2(APP(app(eq, app(s, 0)), app(s, 0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3, c17_2, c45_1, c46_1, c2_1


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), empty)), z0) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), empty), z0)), app(app(app(app(reach, x3), x1), z0), empty)), APP(app(app(app(reach, x0), x1), empty), z0), APP(app(app(app(reach, x3), x1), app(app(union, empty), z0)), empty), APP(app(union, empty), z0)) by 
   APP(app(app(app(app(if_reach_2, false), x0), z1), app(app(app(edge, x2), z0), empty)), empty) -> c49(APP(app(or, app(app(app(app(reach, x0), z1), empty), empty)), false), APP(app(app(app(reach, x0), z1), empty), empty), APP(app(app(app(reach, z0), z1), app(app(union, empty), empty)), empty), APP(app(union, empty), empty))
   APP(app(app(app(app(if_reach_2, false), x0), z1), app(app(app(edge, x2), z0), empty)), app(app(app(edge, z2), z3), z4)) -> c49(APP(app(or, app(app(app(app(reach, x0), z1), empty), app(app(app(edge, z2), z3), z4))), app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), empty)), APP(app(app(app(reach, x0), z1), empty), app(app(app(edge, z2), z3), z4)), APP(app(app(app(reach, z0), z1), app(app(union, empty), app(app(app(edge, z2), z3), z4))), empty), APP(app(union, empty), app(app(app(edge, z2), z3), z4)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), z2), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(eq) -> eq
   encArg(0) -> 0
   encArg(true) -> true
   encArg(s) -> s
   encArg(false) -> false
   encArg(or) -> or
   encArg(union) -> union
   encArg(empty) -> empty
   encArg(edge) -> edge
   encArg(reach) -> reach
   encArg(if_reach_1) -> if_reach_1
   encArg(if_reach_2) -> if_reach_2
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(eq, 0), 0) -> true
   app(app(eq, 0), app(s, z0)) -> false
   app(app(eq, app(s, z0)), 0) -> false
   app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1)
   app(app(or, true), z0) -> true
   app(app(or, false), z0) -> z0
   app(app(union, empty), z0) -> z0
   app(app(union, app(app(app(edge, z0), z1), z2)), z3) -> app(app(app(edge, z0), z1), app(app(union, z2), z3))
   app(app(app(app(reach, z0), z1), empty), z2) -> false
   app(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)
   app(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))
   app(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> true
   app(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))
   app(app(map, z0), nil) -> nil
   app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2))
   app(app(filter, z0), nil) -> nil
   app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)
   app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2))
   app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2)
Tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   ENCARG(cons_app(eq, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(or, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(union, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(empty, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(edge, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(reach, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_1, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(if_reach_2, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c17(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c17(ENCARG(x1))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, or) -> c(APP(encArg(x0), or))
   ENCODE_APP(x0, union) -> c(APP(encArg(x0), union))
   ENCODE_APP(x0, empty) -> c(APP(encArg(x0), empty))
   ENCODE_APP(x0, edge) -> c(APP(encArg(x0), edge))
   ENCODE_APP(x0, reach) -> c(APP(encArg(x0), reach))
   ENCODE_APP(x0, if_reach_1) -> c(APP(encArg(x0), if_reach_1))
   ENCODE_APP(x0, if_reach_2) -> c(APP(encArg(x0), if_reach_2))
   ENCODE_APP(x0, map) -> c(APP(encArg(x0), map))
   ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil))
   ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_app(x0, cons_app(x1, eq))) -> c17(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c17(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c17(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c17(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c17(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, or))) -> c17(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or)))
   ENCARG(cons_app(x0, cons_app(x1, union))) -> c17(APP(encArg(x0), app(encArg(x1), union)), ENCARG(x0), ENCARG(cons_app(x1, union)))
   ENCARG(cons_app(x0, cons_app(x1, empty))) -> c17(APP(encArg(x0), app(encArg(x1), empty)), ENCARG(x0), ENCARG(cons_app(x1, empty)))
   ENCARG(cons_app(x0, cons_app(x1, edge))) -> c17(APP(encArg(x0), app(encArg(x1), edge)), ENCARG(x0), ENCARG(cons_app(x1, edge)))
   ENCARG(cons_app(x0, cons_app(x1, reach))) -> c17(APP(encArg(x0), app(encArg(x1), reach)), ENCARG(x0), ENCARG(cons_app(x1, reach)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_1))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_1)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_1)))
   ENCARG(cons_app(x0, cons_app(x1, if_reach_2))) -> c17(APP(encArg(x0), app(encArg(x1), if_reach_2)), ENCARG(x0), ENCARG(cons_app(x1, if_reach_2)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c17(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c17(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c17(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c17(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c17(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c17(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1))))
   ENCARG(cons_app(x0, cons_app(eq, x2))) -> c17(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c17(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c17(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c17(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c17(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(or, x2))) -> c17(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2)))
   ENCARG(cons_app(x0, cons_app(union, x2))) -> c17(APP(encArg(x0), app(union, encArg(x2))), ENCARG(x0), ENCARG(cons_app(union, x2)))
   ENCARG(cons_app(x0, cons_app(empty, x2))) -> c17(APP(encArg(x0), app(empty, encArg(x2))), ENCARG(x0), ENCARG(cons_app(empty, x2)))
   ENCARG(cons_app(x0, cons_app(edge, x2))) -> c17(APP(encArg(x0), app(edge, encArg(x2))), ENCARG(x0), ENCARG(cons_app(edge, x2)))
   ENCARG(cons_app(x0, cons_app(reach, x2))) -> c17(APP(encArg(x0), app(reach, encArg(x2))), ENCARG(x0), ENCARG(cons_app(reach, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_1, x2))) -> c17(APP(encArg(x0), app(if_reach_1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_1, x2)))
   ENCARG(cons_app(x0, cons_app(if_reach_2, x2))) -> c17(APP(encArg(x0), app(if_reach_2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if_reach_2, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c17(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c17(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c17(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c17(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c17(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c17(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c17(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(eq, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(or, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(union, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(empty, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(edge, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(reach, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_1, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(if_reach_2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c17(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, eq), x2)) -> c17(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c17(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c17(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c17(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c17(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, or), x2)) -> c17(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, union), x2)) -> c17(APP(app(encArg(x0), union), encArg(x2)), ENCARG(cons_app(x0, union)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, empty), x2)) -> c17(APP(app(encArg(x0), empty), encArg(x2)), ENCARG(cons_app(x0, empty)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, edge), x2)) -> c17(APP(app(encArg(x0), edge), encArg(x2)), ENCARG(cons_app(x0, edge)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, reach), x2)) -> c17(APP(app(encArg(x0), reach), encArg(x2)), ENCARG(cons_app(x0, reach)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_1), x2)) -> c17(APP(app(encArg(x0), if_reach_1), encArg(x2)), ENCARG(cons_app(x0, if_reach_1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, if_reach_2), x2)) -> c17(APP(app(encArg(x0), if_reach_2), encArg(x2)), ENCARG(cons_app(x0, if_reach_2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c17(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c17(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c17(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c17(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c17(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c17(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2))
   ENCARG(cons_app(cons_app(eq, x1), x2)) -> c17(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(or, x1), x2)) -> c17(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(union, x1), x2)) -> c17(APP(app(union, encArg(x1)), encArg(x2)), ENCARG(cons_app(union, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c17(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c17(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c17(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, x1), eq)) -> c17(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c17(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c17(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c17(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c17(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), or)) -> c17(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), union)) -> c17(APP(app(encArg(x0), encArg(x1)), union), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), empty)) -> c17(APP(app(encArg(x0), encArg(x1)), empty), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), edge)) -> c17(APP(app(encArg(x0), encArg(x1)), edge), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), reach)) -> c17(APP(app(encArg(x0), encArg(x1)), reach), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_1)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_1), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), if_reach_2)) -> c17(APP(app(encArg(x0), encArg(x1)), if_reach_2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c17(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c17(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c17(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c17(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c17(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c17(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c17(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c17(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c17(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(empty, x1), x2)) -> c17(ENCARG(cons_app(empty, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(edge, x1), x2)) -> c17(ENCARG(cons_app(edge, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(reach, x1), x2)) -> c17(ENCARG(cons_app(reach, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_1, x1), x2)) -> c17(ENCARG(cons_app(if_reach_1, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(if_reach_2, x1), x2)) -> c17(ENCARG(cons_app(if_reach_2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c17(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c17(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c17(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, x1)), app(app(app(edge, x2), app(s, x3)), x4)), x5) -> c46(APP(app(eq, app(s, x1)), app(s, x3)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c2(APP(app(app(app(app(if_reach_2, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c2(APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(app(if_reach_2, false), x0), z1), app(app(app(edge, x2), z0), empty)), empty) -> c49(APP(app(or, app(app(app(app(reach, x0), z1), empty), empty)), false), APP(app(app(app(reach, x0), z1), empty), empty), APP(app(app(app(reach, z0), z1), app(app(union, empty), empty)), empty), APP(app(union, empty), empty))
   APP(app(app(app(app(if_reach_2, false), x0), z1), app(app(app(edge, x2), z0), empty)), app(app(app(edge, z2), z3), z4)) -> c49(APP(app(or, app(app(app(app(reach, x0), z1), empty), app(app(app(edge, z2), z3), z4))), app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), empty)), APP(app(app(app(reach, x0), z1), empty), app(app(app(edge, z2), z3), z4)), APP(app(app(app(reach, z0), z1), app(app(union, empty), app(app(app(edge, z2), z3), z4))), empty), APP(app(union, empty), app(app(app(edge, z2), z3), z4)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), z2), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
S tuples:
   APP(app(eq, 0), 0) -> c36
   APP(app(eq, 0), app(s, z0)) -> c37
   APP(app(eq, app(s, z0)), 0) -> c38
   APP(app(or, true), z0) -> c40
   APP(app(or, false), z0) -> c41
   APP(app(union, empty), z0) -> c42
   APP(app(app(app(reach, z0), z1), empty), z2) -> c44
   APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c48
   APP(app(map, z0), nil) -> c50
   APP(app(filter, z0), nil) -> c52
   APP(app(eq, app(s, z0)), app(s, z1)) -> c39(APP(app(eq, z0), z1))
   APP(app(union, app(app(app(edge, z0), z1), z2)), z3) -> c43(APP(app(union, z2), z3))
   APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5) -> c47(APP(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c51(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c54(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c55(APP(app(filter, z0), z2))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), 0), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, 0), 0))
   APP(app(app(app(reach, 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), 0), x1), app(app(app(edge, app(s, z0)), x3), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(reach, app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, z0)), x1), app(app(app(edge, 0), x3), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), 0), app(app(app(edge, x2), app(s, z0)), x4)), x5), APP(app(eq, 0), app(s, z0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, z0)), app(app(app(edge, x2), 0), x4)), x5), APP(app(eq, app(s, z0)), 0))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(app(app(app(if_reach_2, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), 0), app(app(app(edge, x2), 0), x4)), x5) -> c1(APP(app(eq, 0), 0))
   APP(app(app(app(app(if_reach_2, false), x0), x1), app(app(app(edge, x2), x3), app(app(app(edge, z0), z1), z2))), z3) -> c49(APP(app(or, app(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3)), app(app(app(app(reach, x3), x1), app(app(app(edge, z0), z1), app(app(union, z2), z3))), empty)), APP(app(app(app(reach, x0), x1), app(app(app(edge, z0), z1), z2)), z3), APP(app(app(app(reach, x3), x1), app(app(union, app(app(app(edge, z0), z1), z2)), z3)), empty), APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), app(app(app(edge, z2), z3), z4))), z5) -> c49(APP(app(or, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty)), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5), APP(app(app(app(reach, x3), z1), app(app(union, app(app(app(edge, z2), z3), z4)), z5)), empty), APP(app(union, app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(eq, 0)), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0))
   APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0)))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c53(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0))
   APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c53(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1)))
   APP(app(filter, app(or, true)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, true), app(or, true)), z0), x2), APP(app(or, true), z0))
   APP(app(filter, app(or, false)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(or, false)), z0), x2), APP(app(or, false), z0))
   APP(app(filter, app(union, empty)), app(app(cons, z0), x2)) -> c53(APP(app(app(app(filter2, z0), app(union, empty)), z0), x2), APP(app(union, empty), z0))
   APP(app(filter, app(app(app(reach, z0), z1), empty)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, false), app(app(app(reach, z0), z1), empty)), z2), x2), APP(app(app(app(reach, z0), z1), empty), z2))
   APP(app(filter, app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(reach, z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(app(if_reach_2, app(app(eq, z1), z3)), z0), z1), app(app(app(edge, z2), z3), z4)), z5)), app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(reach, z0), z1), z4), app(app(app(edge, z2), z3), z5))), app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_1, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, true), app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, true), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), app(app(cons, z5), x2)) -> c53(APP(app(app(app(filter2, app(app(or, app(app(app(app(reach, z0), z1), z4), z5)), app(app(app(app(reach, z3), z1), app(app(union, z4), z5)), empty))), app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4))), z5), x2), APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, z2), z3), z4)), z5))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))
   APP(app(filter, app(union, app(app(app(edge, z0), z1), z2))), app(app(cons, z3), x2)) -> c53(APP(app(union, app(app(app(edge, z0), z1), z2)), z3))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c53(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c53(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c53(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c53(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, true), app(s, 0)), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(reach, app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, 0)), x1), app(app(app(edge, app(s, app(s, z0))), x3), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, false), app(s, app(s, z0))), x1), app(app(app(edge, app(s, 0)), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(reach, app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5) -> c45(APP(app(app(app(app(if_reach_1, app(app(eq, z0), z1)), app(s, app(s, z0))), x1), app(app(app(edge, app(s, app(s, z1))), x3), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(reach, app(s, x0)), x1), app(app(app(edge, app(s, x2)), x3), x4)), x5) -> c45(APP(app(eq, app(s, x0)), app(s, x2)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, 0)), app(app(app(edge, x2), app(s, app(s, z0))), x4)), x5), APP(app(eq, app(s, 0)), app(s, app(s, z0))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, false), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, 0)), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, 0)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5) -> c46(APP(app(app(app(app(if_reach_2, app(app(eq, z0), z1)), x0), app(s, app(s, z0))), app(app(app(edge, x2), app(s, app(s, z1))), x4)), x5), APP(app(eq, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, x1)), app(app(app(edge, x2), app(s, x3)), x4)), x5) -> c46(APP(app(eq, app(s, x1)), app(s, x3)))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c2(APP(app(app(app(app(if_reach_2, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5))
   APP(app(app(app(app(if_reach_1, true), x0), app(s, 0)), app(app(app(edge, x2), app(s, 0)), x4)), x5) -> c2(APP(app(eq, app(s, 0)), app(s, 0)))
   APP(app(app(app(app(if_reach_2, false), x0), z1), app(app(app(edge, x2), z0), empty)), empty) -> c49(APP(app(or, app(app(app(app(reach, x0), z1), empty), empty)), false), APP(app(app(app(reach, x0), z1), empty), empty), APP(app(app(app(reach, z0), z1), app(app(union, empty), empty)), empty), APP(app(union, empty), empty))
   APP(app(app(app(app(if_reach_2, false), x0), z1), app(app(app(edge, x2), z0), empty)), app(app(app(edge, z2), z3), z4)) -> c49(APP(app(or, app(app(app(app(reach, x0), z1), empty), app(app(app(edge, z2), z3), z4))), app(app(app(app(app(if_reach_1, app(app(eq, z0), z2)), z0), z1), app(app(app(edge, z2), z3), z4)), empty)), APP(app(app(app(reach, x0), z1), empty), app(app(app(edge, z2), z3), z4)), APP(app(app(app(reach, z0), z1), app(app(union, empty), app(app(app(edge, z2), z3), z4))), empty), APP(app(union, empty), app(app(app(edge, z2), z3), z4)))
   APP(app(app(app(app(if_reach_2, false), z0), z1), app(app(app(edge, x2), x3), empty)), z2) -> c49(APP(app(or, false), app(app(app(app(reach, x3), z1), z2), empty)), APP(app(app(app(reach, z0), z1), empty), z2), APP(app(app(app(reach, x3), z1), app(app(union, empty), z2)), empty), APP(app(union, empty), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c36, c37, c38, c40, c41, c42, c44, c48, c50, c52, c39_1, c43_1, c47_1, c51_2, c54_1, c55_1, c17_1, c45_2, c46_2, c1_1, c49_4, c53_2, c53_1, c_1, c17_3, c17_2, c45_1, c46_1, c2_1