/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 215 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(12) TRS for Loop Detection
(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), 47 ms]
        (24) CpxTypedWeightedCompleteTrs
        (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 35 ms]
        (26) CpxRNTS
        (27) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (28) CpxRNTS
    (29) CompletionProof [UPPER BOUND(ID), 0 ms]
    (30) CpxTypedWeightedCompleteTrs
        (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 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), 5 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), 0 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms]
    (46) CdtProblem
    (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (52) CdtProblem
    (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 101 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 95 ms]
    (64) CdtProblem
    (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms]
    (68) CdtProblem
    (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms]
    (72) CdtProblem
    (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms]
    (80) CdtProblem
    (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
    (84) CdtProblem
    (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms]
    (88) CdtProblem
    (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms]
    (96) CdtProblem
    (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (100) CdtProblem
    (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 6 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms]
    (106) CdtProblem
    (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 65 ms]
    (120) CdtProblem
    (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 15 ms]
    (122) CdtProblem
    (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms]
    (124) CdtProblem
    (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms]
    (134) CdtProblem
    (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms]
    (146) CdtProblem
    (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
    (148) CdtProblem
    (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
    (152) CdtProblem
    (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CdtProblem
    (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
    (156) CdtProblem
    (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
    (160) CdtProblem
    (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) 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(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
   app(app(quot, 0), app(s, y)) -> 0
   app(app(quot, app(s, x)), app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
   app(app(plus, 0), y) -> y
   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
   app(app(plus, app(app(minus, x), app(s, 0))), app(app(minus, y), app(s, app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0)))
   app(app(plus, app(app(plus, x), app(s, 0))), app(app(plus, y), app(s, app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0)))
   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(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   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_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false


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

(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(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
   app(app(quot, 0), app(s, y)) -> 0
   app(app(quot, app(s, x)), app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
   app(app(plus, 0), y) -> y
   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
   app(app(plus, app(app(minus, x), app(s, 0))), app(app(minus, y), app(s, app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0)))
   app(app(plus, app(app(plus, x), app(s, 0))), app(app(plus, y), app(s, app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0)))
   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(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   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_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
   app(app(quot, 0), app(s, y)) -> 0
   app(app(quot, app(s, x)), app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
   app(app(plus, 0), y) -> y
   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
   app(app(plus, app(app(minus, x), app(s, 0))), app(app(minus, y), app(s, app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0)))
   app(app(plus, app(app(plus, x), app(s, 0))), app(app(plus, y), app(s, app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0)))
   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(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   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_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

(6)
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(minus, x), 0') -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
   app(app(quot, 0'), app(s, y)) -> 0'
   app(app(quot, app(s, x)), app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
   app(app(plus, 0'), y) -> y
   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
   app(app(plus, app(app(minus, x), app(s, 0'))), app(app(minus, y), app(s, app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0')))
   app(app(plus, app(app(plus, x), app(s, 0'))), app(app(plus, y), app(s, app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0')))
   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(minus) -> minus
   encArg(0') -> 0'
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   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_minus -> minus
   encode_0 -> 0'
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

(8)
Obligation:
Innermost TRS:
Rules:
app(app(minus, x), 0') -> x
app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
app(app(quot, 0'), app(s, y)) -> 0'
app(app(quot, app(s, x)), app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
app(app(plus, 0'), y) -> y
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
app(app(plus, app(app(minus, x), app(s, 0'))), app(app(minus, y), app(s, app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0')))
app(app(plus, app(app(plus, x), app(s, 0'))), app(app(plus, y), app(s, app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0')))
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(minus) -> minus
encArg(0') -> 0'
encArg(s) -> s
encArg(quot) -> quot
encArg(plus) -> plus
encArg(map) -> map
encArg(nil) -> nil
encArg(cons) -> cons
encArg(filter) -> filter
encArg(filter2) -> filter2
encArg(true) -> true
encArg(false) -> false
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_minus -> minus
encode_0 -> 0'
encode_s -> s
encode_quot -> quot
encode_plus -> plus
encode_map -> map
encode_nil -> nil
encode_cons -> cons
encode_filter -> filter
encode_filter2 -> filter2
encode_true -> true
encode_false -> false

Types:
app :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
minus :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
0' :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
s :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
quot :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
plus :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
map :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
nil :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
cons :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
filter :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
filter2 :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
true :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
false :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encArg :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
cons_app :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_app :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_minus :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_0 :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_s :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_quot :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_plus :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_map :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_nil :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_cons :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter2 :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_true :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_false :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
hole_minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app1_3 :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
gen_minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app2_3 :: Nat -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app

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

(9) 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

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

(10)
Obligation:
Innermost TRS:
Rules:
app(app(minus, x), 0') -> x
app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
app(app(quot, 0'), app(s, y)) -> 0'
app(app(quot, app(s, x)), app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
app(app(plus, 0'), y) -> y
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
app(app(plus, app(app(minus, x), app(s, 0'))), app(app(minus, y), app(s, app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0')))
app(app(plus, app(app(plus, x), app(s, 0'))), app(app(plus, y), app(s, app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0')))
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(minus) -> minus
encArg(0') -> 0'
encArg(s) -> s
encArg(quot) -> quot
encArg(plus) -> plus
encArg(map) -> map
encArg(nil) -> nil
encArg(cons) -> cons
encArg(filter) -> filter
encArg(filter2) -> filter2
encArg(true) -> true
encArg(false) -> false
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_minus -> minus
encode_0 -> 0'
encode_s -> s
encode_quot -> quot
encode_plus -> plus
encode_map -> map
encode_nil -> nil
encode_cons -> cons
encode_filter -> filter
encode_filter2 -> filter2
encode_true -> true
encode_false -> false

Types:
app :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
minus :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
0' :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
s :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
quot :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
plus :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
map :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
nil :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
cons :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
filter :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
filter2 :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
true :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
false :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encArg :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
cons_app :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_app :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_minus :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_0 :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_s :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_quot :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_plus :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_map :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_nil :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_cons :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter2 :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_true :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
encode_false :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
hole_minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app1_3 :: minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app
gen_minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app2_3 :: Nat -> minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app


Generator Equations:
gen_minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app2_3(0) <=> minus
gen_minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false:cons_app2_3(+(x, 1)) <=> cons_app(minus, gen_minus:0':s:quot:plus:map:nil:cons:filter:filter2:true:false: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

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

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

(12)
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(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
   app(app(quot, 0), app(s, y)) -> 0
   app(app(quot, app(s, x)), app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
   app(app(plus, 0), y) -> y
   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
   app(app(plus, app(app(minus, x), app(s, 0))), app(app(minus, y), app(s, app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0)))
   app(app(plus, app(app(plus, x), app(s, 0))), app(app(plus, y), app(s, app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0)))
   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(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   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_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

(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(minus, x), 0) -> x
   app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
   app(app(quot, 0), app(s, y)) -> 0
   app(app(quot, app(s, x)), app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
   app(app(plus, 0), y) -> y
   app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
   app(app(plus, app(app(minus, x), app(s, 0))), app(app(minus, y), app(s, app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0)))
   app(app(plus, app(app(plus, x), app(s, 0))), app(app(plus, y), app(s, app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0)))
   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(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   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_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs)
   app(c_app(map, f), nil) -> nil
   app(c_app(filter, f), nil) -> nil
   app(c_app(minus, x), 0) -> x
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0)))
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y)))
   app(c_app(plus, c_app(s, x)), y) -> app(s, app(app(plus, x), y))
   app(c_app(quot, 0), c_app(s, y)) -> 0
   app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
   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(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y)
   app(c_app(plus, 0), y) -> y
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0)))

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

   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   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_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   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(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0))) [1]
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y))) [1]
   app(c_app(plus, c_app(s, x)), y) -> app(s, app(app(plus, x), y)) [1]
   app(c_app(quot, 0), c_app(s, y)) -> 0 [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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [1]
   app(c_app(plus, 0), y) -> y [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0))) [1]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(plus) -> plus [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(true) -> true [0]
   encArg(false) -> false [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_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_quot -> quot [0]
   encode_plus -> plus [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   encode_true -> true [0]
   encode_false -> false [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(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0))) [1]
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y))) [1]
   app(c_app(plus, c_app(s, x)), y) -> app(s, app(app(plus, x), y)) [1]
   app(c_app(quot, 0), c_app(s, y)) -> 0 [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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [1]
   app(c_app(plus, 0), y) -> y [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0))) [1]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(plus) -> plus [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(true) -> true [0]
   encArg(false) -> false [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_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_quot -> quot [0]
   encode_plus -> plus [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   encode_true -> true [0]
   encode_false -> false [0]
   app(x0, x1) -> c_app(x0, x1) [0]

The TRS has the following type information:
app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
c_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encArg :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
cons_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app
encode_false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true: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_minus
   encode_0
   encode_s
   encode_quot
   encode_plus
   encode_map
   encode_nil
   encode_cons
   encode_filter
   encode_filter2
   encode_true
   encode_false
   app_2

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_quot -> null_encode_quot [0]
   encode_plus -> null_encode_plus [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]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_minus, null_encode_0, null_encode_s, null_encode_quot, null_encode_plus, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, 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(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0))) [1]
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y))) [1]
   app(c_app(plus, c_app(s, x)), y) -> app(s, app(app(plus, x), y)) [1]
   app(c_app(quot, 0), c_app(s, y)) -> 0 [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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [1]
   app(c_app(plus, 0), y) -> y [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0))) [1]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(plus) -> plus [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(true) -> true [0]
   encArg(false) -> false [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_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_quot -> quot [0]
   encode_plus -> plus [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   encode_true -> true [0]
   encode_false -> false [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_quot -> null_encode_quot [0]
   encode_plus -> null_encode_plus [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]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
c_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encArg :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false: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(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(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(minus, y), app(s, c_app(s, z)))), app(c_app(minus, x), c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(minus, y), app(s, c_app(s, z)))), app(c_app(minus, x), null_app)) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(minus, y), app(s, c_app(s, z)))), app(null_app, c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(minus, y), app(s, c_app(s, z)))), app(null_app, null_app)) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(minus, y), app(s, null_app))), app(c_app(minus, x), c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(minus, y), app(s, null_app))), app(c_app(minus, x), null_app)) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(minus, y), app(s, null_app))), app(null_app, c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(minus, y), app(s, null_app))), app(null_app, null_app)) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, c_app(s, z)))), app(c_app(minus, x), c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, c_app(s, z)))), app(c_app(minus, x), null_app)) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, c_app(s, z)))), app(null_app, c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, c_app(s, z)))), app(null_app, null_app)) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, null_app))), app(c_app(minus, x), c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, null_app))), app(c_app(minus, x), null_app)) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, null_app))), app(null_app, c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, null_app))), app(null_app, null_app)) [1]
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(c_app(minus, x), y)), c_app(s, y))) [1]
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(c_app(minus, x), y)), null_app)) [1]
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(null_app, y)), c_app(s, y))) [1]
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(null_app, y)), null_app)) [1]
   app(c_app(plus, c_app(s, x)), y) -> app(s, app(c_app(plus, x), y)) [1]
   app(c_app(plus, c_app(s, x)), y) -> app(s, app(null_app, y)) [1]
   app(c_app(quot, 0), c_app(s, y)) -> 0 [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(filter, c_app(map, f5)), c_app(c_app(cons, c_app(c_app(cons, x10), xs1)), xs)) -> app(app(app(app(filter2, app(app(cons, app(f5, x10)), app(app(map, f5), xs1))), c_app(map, f5)), c_app(c_app(cons, x10), xs1)), xs) [2]
   app(c_app(filter, c_app(c_app(c_app(filter2, false), f6), x11)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(filter, f6), x)), c_app(c_app(c_app(filter2, false), f6), x11)), x), xs) [2]
   app(c_app(filter, c_app(map, f7)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(map, f7)), nil), xs) [2]
   app(c_app(filter, c_app(filter, f8)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(filter, f8)), nil), xs) [2]
   app(c_app(filter, c_app(minus, x12)), c_app(c_app(cons, 0), xs)) -> app(app(app(app(filter2, x12), c_app(minus, x12)), 0), xs) [2]
   app(c_app(filter, c_app(plus, c_app(c_app(minus, x13), c_app(s, 0)))), c_app(c_app(cons, c_app(c_app(minus, y4), c_app(s, c_app(s, z1)))), xs)) -> app(app(app(app(filter2, app(app(plus, app(app(minus, y4), app(s, app(s, z1)))), app(app(minus, x13), app(s, 0)))), c_app(plus, c_app(c_app(minus, x13), c_app(s, 0)))), c_app(c_app(minus, y4), c_app(s, c_app(s, z1)))), xs) [2]
   app(c_app(filter, c_app(quot, c_app(s, x14))), c_app(c_app(cons, c_app(s, y5)), xs)) -> app(app(app(app(filter2, app(s, app(app(quot, app(app(minus, x14), y5)), app(s, y5)))), c_app(quot, c_app(s, x14))), c_app(s, y5)), xs) [2]
   app(c_app(filter, c_app(plus, c_app(s, x15))), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(s, app(app(plus, x15), x))), c_app(plus, c_app(s, x15))), x), xs) [2]
   app(c_app(filter, c_app(quot, 0)), c_app(c_app(cons, c_app(s, y6)), xs)) -> app(app(app(app(filter2, 0), c_app(quot, 0)), c_app(s, y6)), xs) [2]
   app(c_app(filter, c_app(c_app(c_app(filter2, true), f9), x16)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(cons, x16), app(app(filter, f9), x))), c_app(c_app(c_app(filter2, true), f9), x16)), x), xs) [2]
   app(c_app(filter, c_app(filter, f10)), c_app(c_app(cons, c_app(c_app(cons, x17), xs2)), xs)) -> app(app(app(app(filter2, app(app(app(app(filter2, app(f10, x17)), f10), x17), xs2)), c_app(filter, f10)), c_app(c_app(cons, x17), xs2)), xs) [2]
   app(c_app(filter, c_app(minus, c_app(s, x18))), c_app(c_app(cons, c_app(s, y7)), xs)) -> app(app(app(app(filter2, app(app(minus, x18), y7)), c_app(minus, c_app(s, x18))), c_app(s, y7)), xs) [2]
   app(c_app(filter, c_app(plus, 0)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, x), c_app(plus, 0)), x), xs) [2]
   app(c_app(filter, c_app(plus, c_app(c_app(plus, x19), c_app(s, 0)))), c_app(c_app(cons, c_app(c_app(plus, y8), c_app(s, c_app(s, z2)))), xs)) -> app(app(app(app(filter2, app(app(plus, app(app(plus, y8), app(s, app(s, z2)))), app(app(plus, x19), app(s, 0)))), c_app(plus, c_app(c_app(plus, x19), c_app(s, 0)))), c_app(c_app(plus, y8), c_app(s, c_app(s, z2)))), xs) [2]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, c_app(f, x)), f), x), xs) [1]
   app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, null_app), f), x), xs) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(c_app(minus, x), y) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(null_app, y) [1]
   app(c_app(plus, 0), y) -> y [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(plus, y), app(s, c_app(s, z)))), app(c_app(plus, x), c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(plus, y), app(s, c_app(s, z)))), app(c_app(plus, x), null_app)) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(plus, y), app(s, c_app(s, z)))), app(null_app, c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(plus, y), app(s, c_app(s, z)))), app(null_app, null_app)) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(plus, y), app(s, null_app))), app(c_app(plus, x), c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(plus, y), app(s, null_app))), app(c_app(plus, x), null_app)) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(plus, y), app(s, null_app))), app(null_app, c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(c_app(plus, y), app(s, null_app))), app(null_app, null_app)) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, c_app(s, z)))), app(c_app(plus, x), c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, c_app(s, z)))), app(c_app(plus, x), null_app)) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, c_app(s, z)))), app(null_app, c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, c_app(s, z)))), app(null_app, null_app)) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, null_app))), app(c_app(plus, x), c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, null_app))), app(c_app(plus, x), null_app)) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, null_app))), app(null_app, c_app(s, 0))) [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(null_app, app(s, null_app))), app(null_app, null_app)) [1]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(plus) -> plus [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(true) -> true [0]
   encArg(false) -> false [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_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_quot -> quot [0]
   encode_plus -> plus [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   encode_true -> true [0]
   encode_false -> false [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_quot -> null_encode_quot [0]
   encode_plus -> null_encode_plus [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]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
c_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encArg :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false: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 => 5
   cons => 1
   filter2 => 4
   false => 2
   filter => 3
   nil => 7
   minus => 6
   0 => 0
   plus => 8
   s => 10
   quot => 9
   true => 11
   null_encArg => 0
   null_encode_app => 0
   null_encode_minus => 0
   null_encode_0 => 0
   null_encode_s => 0
   null_encode_quot => 0
   null_encode_plus => 0
   null_encode_map => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_filter => 0
   null_encode_filter2 => 0
   null_encode_true => 0
   null_encode_false => 0
   null_app => 0

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

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

   app(z', z'') -{ 1 }-> x :|: z'' = 0, x >= 0, z' = 1 + 6 + x
   app(z', z'') -{ 1 }-> y :|: z' = 1 + 8 + 0, z'' = y, y >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, x), 1 + 8 + 0), x), xs) :|: z' = 1 + 3 + (1 + 8 + 0), xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 2 }-> app(app(app(app(4, x12), 1 + 6 + x12), 0), xs) :|: xs >= 0, z'' = 1 + (1 + 1 + 0) + xs, x12 >= 0, z' = 1 + 3 + (1 + 6 + x12)
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(app(app(4, app(f10, x17)), f10), x17), xs2)), 1 + 3 + f10), 1 + (1 + 1 + x17) + xs2), xs) :|: z'' = 1 + (1 + 1 + (1 + (1 + 1 + x17) + xs2)) + xs, xs >= 0, x17 >= 0, xs2 >= 0, f10 >= 0, z' = 1 + 3 + (1 + 3 + f10)
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(8, app(app(8, y8), app(10, app(10, z2)))), app(app(8, x19), app(10, 0)))), 1 + 8 + (1 + (1 + 8 + x19) + (1 + 10 + 0))), 1 + (1 + 8 + y8) + (1 + 10 + (1 + 10 + z2))), xs) :|: xs >= 0, y8 >= 0, x19 >= 0, z'' = 1 + (1 + 1 + (1 + (1 + 8 + y8) + (1 + 10 + (1 + 10 + z2)))) + xs, z' = 1 + 3 + (1 + 8 + (1 + (1 + 8 + x19) + (1 + 10 + 0))), z2 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(8, app(app(6, y4), app(10, app(10, z1)))), app(app(6, x13), app(10, 0)))), 1 + 8 + (1 + (1 + 6 + x13) + (1 + 10 + 0))), 1 + (1 + 6 + y4) + (1 + 10 + (1 + 10 + z1))), xs) :|: z' = 1 + 3 + (1 + 8 + (1 + (1 + 6 + x13) + (1 + 10 + 0))), x13 >= 0, xs >= 0, z1 >= 0, z'' = 1 + (1 + 1 + (1 + (1 + 6 + y4) + (1 + 10 + (1 + 10 + z1)))) + xs, y4 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(6, x18), y7)), 1 + 6 + (1 + 10 + x18)), 1 + 10 + y7), xs) :|: xs >= 0, z' = 1 + 3 + (1 + 6 + (1 + 10 + x18)), y7 >= 0, x18 >= 0, z'' = 1 + (1 + 1 + (1 + 10 + y7)) + xs
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(3, f6), x)), 1 + (1 + (1 + 4 + 2) + f6) + x11), x), xs) :|: z' = 1 + 3 + (1 + (1 + (1 + 4 + 2) + f6) + x11), xs >= 0, x >= 0, f6 >= 0, x11 >= 0, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(1, x16), app(app(3, f9), x))), 1 + (1 + (1 + 4 + 11) + f9) + x16), x), xs) :|: z' = 1 + 3 + (1 + (1 + (1 + 4 + 11) + f9) + x16), xs >= 0, x >= 0, f9 >= 0, z'' = 1 + (1 + 1 + x) + xs, x16 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(1, app(f5, x10)), app(app(5, f5), xs1))), 1 + 5 + f5), 1 + (1 + 1 + x10) + xs1), xs) :|: xs >= 0, z' = 1 + 3 + (1 + 5 + f5), z'' = 1 + (1 + 1 + (1 + (1 + 1 + x10) + xs1)) + xs, xs1 >= 0, f5 >= 0, x10 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(10, app(app(9, app(app(6, x14), y5)), app(10, y5)))), 1 + 9 + (1 + 10 + x14)), 1 + 10 + y5), xs) :|: y5 >= 0, xs >= 0, z'' = 1 + (1 + 1 + (1 + 10 + y5)) + xs, x14 >= 0, z' = 1 + 3 + (1 + 9 + (1 + 10 + x14))
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(10, app(app(8, x15), x))), 1 + 8 + (1 + 10 + x15)), x), xs) :|: xs >= 0, z' = 1 + 3 + (1 + 8 + (1 + 10 + x15)), x >= 0, z'' = 1 + (1 + 1 + x) + xs, x15 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, 7), 1 + 5 + f7), 7), xs) :|: xs >= 0, f7 >= 0, z'' = 1 + (1 + 1 + 7) + xs, z' = 1 + 3 + (1 + 5 + f7)
   app(z', z'') -{ 2 }-> app(app(app(app(4, 7), 1 + 3 + f8), 7), xs) :|: f8 >= 0, xs >= 0, z'' = 1 + (1 + 1 + 7) + xs, z' = 1 + 3 + (1 + 3 + f8)
   app(z', z'') -{ 1 }-> app(app(app(app(4, 0), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs, z' = 1 + 3 + f
   app(z', z'') -{ 2 }-> app(app(app(app(4, 0), 1 + 9 + 0), 1 + 10 + y6), xs) :|: z'' = 1 + (1 + 1 + (1 + 10 + y6)) + xs, xs >= 0, y6 >= 0, z' = 1 + 3 + (1 + 9 + 0)
   app(z', z'') -{ 1 }-> app(app(app(app(4, 1 + f + x), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs, z' = 1 + 3 + f
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(0, 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(0, 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(0, 1 + 10 + 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(0, 1 + 10 + 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(1 + 8 + x, 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(1 + 8 + x, 1 + 10 + 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(1 + 6 + x, 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(1 + 6 + x, 1 + 10 + 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(0, 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(0, 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(0, 1 + 10 + 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(0, 1 + 10 + 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(1 + 8 + x, 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(1 + 8 + x, 1 + 10 + 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(1 + 6 + x, 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(1 + 6 + x, 1 + 10 + 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 0))), app(0, 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 0))), app(0, 1 + 10 + 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 0))), app(1 + 8 + x, 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 0))), app(1 + 8 + x, 1 + 10 + 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 1 + 10 + z))), app(0, 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 1 + 10 + z))), app(0, 1 + 10 + 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 1 + 10 + z))), app(1 + 8 + x, 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 1 + 10 + z))), app(1 + 8 + x, 1 + 10 + 0)) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 0))), app(0, 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 0))), app(0, 1 + 10 + 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 0))), app(1 + 6 + x, 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 0))), app(1 + 6 + x, 1 + 10 + 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 1 + 10 + z))), app(0, 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 1 + 10 + z))), app(0, 1 + 10 + 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 1 + 10 + z))), app(1 + 6 + x, 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 1 + 10 + z))), app(1 + 6 + x, 1 + 10 + 0)) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(1, app(f, x)), app(app(5, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z' = 1 + 5 + f, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(0, y)), 0)) :|: x >= 0, y >= 0, z' = 1 + 9 + (1 + 10 + x), z'' = 1 + 10 + y
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(0, y)), 1 + 10 + y)) :|: x >= 0, y >= 0, z' = 1 + 9 + (1 + 10 + x), z'' = 1 + 10 + y
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(1 + 6 + x, y)), 0)) :|: x >= 0, y >= 0, z' = 1 + 9 + (1 + 10 + x), z'' = 1 + 10 + y
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(1 + 6 + x, y)), 1 + 10 + y)) :|: x >= 0, y >= 0, z' = 1 + 9 + (1 + 10 + x), z'' = 1 + 10 + y
   app(z', z'') -{ 1 }-> app(10, app(0, y)) :|: z'' = y, x >= 0, y >= 0, z' = 1 + 8 + (1 + 10 + x)
   app(z', z'') -{ 1 }-> app(10, app(1 + 8 + x, y)) :|: z'' = y, x >= 0, y >= 0, z' = 1 + 8 + (1 + 10 + x)
   app(z', z'') -{ 1 }-> app(0, xs) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 4 + 2) + f) + x
   app(z', z'') -{ 1 }-> app(0, y) :|: z' = 1 + 6 + (1 + 10 + x), x >= 0, y >= 0, z'' = 1 + 10 + y
   app(z', z'') -{ 1 }-> app(0, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> app(0, app(1 + 3 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> app(1 + 6 + x, y) :|: z' = 1 + 6 + (1 + 10 + x), x >= 0, y >= 0, z'' = 1 + 10 + y
   app(z', z'') -{ 1 }-> app(1 + 3 + f, xs) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 4 + 2) + f) + x
   app(z', z'') -{ 1 }-> app(1 + 1 + x, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> app(1 + 1 + x, app(1 + 3 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> 7 :|: f >= 0, z'' = 7, z' = 1 + 5 + f
   app(z', z'') -{ 1 }-> 7 :|: f >= 0, z'' = 7, z' = 1 + 3 + f
   app(z', z'') -{ 1 }-> 0 :|: z' = 1 + 9 + 0, y >= 0, z'' = 1 + 10 + y
   app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   app(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0
   encArg(z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2
   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 }-> 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, z' = x_1, x_2 >= 0, z'' = x_2
   encode_app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 4 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 5 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 6 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 7 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_plus -{ 0 }-> 8 :|: 
   encode_plus -{ 0 }-> 0 :|: 
   encode_quot -{ 0 }-> 9 :|: 
   encode_quot -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 10 :|: 
   encode_s -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 11 :|: 
   encode_true -{ 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 + 8 + 0, z'' >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, x), 1 + 8 + 0), x), xs) :|: z' = 1 + 3 + (1 + 8 + 0), xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(app(app(4, app(z' - 8, x17)), z' - 8), x17), xs2)), 1 + 3 + (z' - 8)), 1 + (1 + 1 + x17) + xs2), xs) :|: z'' = 1 + (1 + 1 + (1 + (1 + 1 + x17) + xs2)) + xs, xs >= 0, x17 >= 0, xs2 >= 0, z' - 8 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(8, app(app(8, y8), app(10, app(10, z2)))), app(app(8, z' - 34), app(10, 0)))), 1 + 8 + (1 + (1 + 8 + (z' - 34)) + (1 + 10 + 0))), 1 + (1 + 8 + y8) + (1 + 10 + (1 + 10 + z2))), xs) :|: xs >= 0, y8 >= 0, z' - 34 >= 0, z'' = 1 + (1 + 1 + (1 + (1 + 8 + y8) + (1 + 10 + (1 + 10 + z2)))) + xs, z2 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(8, app(app(6, y4), app(10, app(10, z1)))), app(app(6, z' - 32), app(10, 0)))), 1 + 8 + (1 + (1 + 6 + (z' - 32)) + (1 + 10 + 0))), 1 + (1 + 6 + y4) + (1 + 10 + (1 + 10 + z1))), xs) :|: z' - 32 >= 0, xs >= 0, z1 >= 0, z'' = 1 + (1 + 1 + (1 + (1 + 6 + y4) + (1 + 10 + (1 + 10 + z1)))) + xs, y4 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(6, z' - 22), y7)), 1 + 6 + (1 + 10 + (z' - 22))), 1 + 10 + y7), xs) :|: xs >= 0, y7 >= 0, z' - 22 >= 0, z'' = 1 + (1 + 1 + (1 + 10 + y7)) + xs
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(3, f6), x)), 1 + (1 + (1 + 4 + 2) + f6) + x11), x), xs) :|: z' = 1 + 3 + (1 + (1 + (1 + 4 + 2) + f6) + x11), xs >= 0, x >= 0, f6 >= 0, x11 >= 0, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(1, x16), app(app(3, f9), x))), 1 + (1 + (1 + 4 + 11) + f9) + x16), x), xs) :|: z' = 1 + 3 + (1 + (1 + (1 + 4 + 11) + f9) + x16), xs >= 0, x >= 0, f9 >= 0, z'' = 1 + (1 + 1 + x) + xs, x16 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(app(1, app(z' - 10, x10)), app(app(5, z' - 10), xs1))), 1 + 5 + (z' - 10)), 1 + (1 + 1 + x10) + xs1), xs) :|: xs >= 0, z'' = 1 + (1 + 1 + (1 + (1 + 1 + x10) + xs1)) + xs, xs1 >= 0, z' - 10 >= 0, x10 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(10, app(app(9, app(app(6, z' - 25), y5)), app(10, y5)))), 1 + 9 + (1 + 10 + (z' - 25))), 1 + 10 + y5), xs) :|: y5 >= 0, xs >= 0, z'' = 1 + (1 + 1 + (1 + 10 + y5)) + xs, z' - 25 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, app(10, app(app(8, z' - 24), x))), 1 + 8 + (1 + 10 + (z' - 24))), x), xs) :|: xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs, z' - 24 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, 7), 1 + 5 + (z' - 10)), 7), z'' - 10) :|: z'' - 10 >= 0, z' - 10 >= 0
   app(z', z'') -{ 2 }-> app(app(app(app(4, 7), 1 + 3 + (z' - 8)), 7), z'' - 10) :|: z' - 8 >= 0, z'' - 10 >= 0
   app(z', z'') -{ 1 }-> app(app(app(app(4, 0), z' - 4), x), xs) :|: z' - 4 >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 2 }-> app(app(app(app(4, 0), 1 + 9 + 0), 1 + 10 + y6), xs) :|: z'' = 1 + (1 + 1 + (1 + 10 + y6)) + xs, xs >= 0, y6 >= 0, z' = 1 + 3 + (1 + 9 + 0)
   app(z', z'') -{ 2 }-> app(app(app(app(4, z' - 11), 1 + 6 + (z' - 11)), 0), z'' - 3) :|: z'' - 3 >= 0, z' - 11 >= 0
   app(z', z'') -{ 1 }-> app(app(app(app(4, 1 + (z' - 4) + x), z' - 4), x), xs) :|: z' - 4 >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(0, 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(0, 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(0, 1 + 10 + 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(0, 1 + 10 + 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(1 + 8 + (z' - 30), 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(1 + 8 + (z' - 30), 1 + 10 + 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(1 + 6 + (z' - 28), 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 0))), app(1 + 6 + (z' - 28), 1 + 10 + 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(0, 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(0, 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(0, 1 + 10 + 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(0, 1 + 10 + 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(1 + 8 + (z' - 30), 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(1 + 8 + (z' - 30), 1 + 10 + 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(1 + 6 + (z' - 28), 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(0, app(10, 1 + 10 + z))), app(1 + 6 + (z' - 28), 1 + 10 + 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 0))), app(0, 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 0))), app(0, 1 + 10 + 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 0))), app(1 + 8 + (z' - 30), 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 0))), app(1 + 8 + (z' - 30), 1 + 10 + 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 1 + 10 + z))), app(0, 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 1 + 10 + z))), app(0, 1 + 10 + 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 1 + 10 + z))), app(1 + 8 + (z' - 30), 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 8 + y, app(10, 1 + 10 + z))), app(1 + 8 + (z' - 30), 1 + 10 + 0)) :|: z >= 0, z' - 30 >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 0))), app(0, 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 0))), app(0, 1 + 10 + 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 0))), app(1 + 6 + (z' - 28), 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 0))), app(1 + 6 + (z' - 28), 1 + 10 + 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 1 + 10 + z))), app(0, 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 1 + 10 + z))), app(0, 1 + 10 + 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 1 + 10 + z))), app(1 + 6 + (z' - 28), 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(1 + 6 + y, app(10, 1 + 10 + z))), app(1 + 6 + (z' - 28), 1 + 10 + 0)) :|: z >= 0, z' - 28 >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(1, app(z' - 6, x)), app(app(5, z' - 6), xs)) :|: z' - 6 >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(0, z'' - 11)), 0)) :|: z' - 21 >= 0, z'' - 11 >= 0
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(0, z'' - 11)), 1 + 10 + (z'' - 11))) :|: z' - 21 >= 0, z'' - 11 >= 0
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(1 + 6 + (z' - 21), z'' - 11)), 0)) :|: z' - 21 >= 0, z'' - 11 >= 0
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(1 + 6 + (z' - 21), z'' - 11)), 1 + 10 + (z'' - 11))) :|: z' - 21 >= 0, z'' - 11 >= 0
   app(z', z'') -{ 1 }-> app(10, app(0, z'')) :|: z' - 20 >= 0, z'' >= 0
   app(z', z'') -{ 1 }-> app(10, app(1 + 8 + (z' - 20), z'')) :|: z' - 20 >= 0, z'' >= 0
   app(z', z'') -{ 1 }-> app(0, z'') :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 4 + 2) + f) + x
   app(z', z'') -{ 1 }-> app(0, app(0, z'')) :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> app(0, app(1 + 3 + f, z'')) :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> app(0, z'' - 11) :|: z' - 18 >= 0, z'' - 11 >= 0
   app(z', z'') -{ 1 }-> app(1 + 6 + (z' - 18), z'' - 11) :|: z' - 18 >= 0, z'' - 11 >= 0
   app(z', z'') -{ 1 }-> app(1 + 3 + f, z'') :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 4 + 2) + f) + x
   app(z', z'') -{ 1 }-> app(1 + 1 + x, app(0, z'')) :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> app(1 + 1 + x, app(1 + 3 + f, z'')) :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> 7 :|: z' - 6 >= 0, z'' = 7
   app(z', z'') -{ 1 }-> 7 :|: z' - 4 >= 0, z'' = 7
   app(z', z'') -{ 1 }-> 0 :|: z' = 1 + 9 + 0, z'' - 11 >= 0
   app(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0
   app(z', z'') -{ 1 }-> z' - 7 :|: z'' = 0, z' - 7 >= 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, x_2 >= 0, z' = 1 + x_1 + x_2
   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 }-> 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_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 4 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 5 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 6 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 7 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_plus -{ 0 }-> 8 :|: 
   encode_plus -{ 0 }-> 0 :|: 
   encode_quot -{ 0 }-> 9 :|: 
   encode_quot -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 10 :|: 
   encode_s -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 11 :|: 
   encode_true -{ 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_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_quot -> null_encode_quot [0]
   encode_plus -> null_encode_plus [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]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   app(v0, v1) -> null_app [0]

And the following fresh constants:    null_encArg, null_encode_app, null_encode_minus, null_encode_0, null_encode_s, null_encode_quot, null_encode_plus, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, 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(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1]
   app(c_app(map, f), nil) -> nil [1]
   app(c_app(filter, f), nil) -> nil [1]
   app(c_app(minus, x), 0) -> x [1]
   app(c_app(plus, c_app(c_app(minus, x), c_app(s, 0))), c_app(c_app(minus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(minus, y), app(s, app(s, z)))), app(app(minus, x), app(s, 0))) [1]
   app(c_app(quot, c_app(s, x)), c_app(s, y)) -> app(s, app(app(quot, app(app(minus, x), y)), app(s, y))) [1]
   app(c_app(plus, c_app(s, x)), y) -> app(s, app(app(plus, x), y)) [1]
   app(c_app(quot, 0), c_app(s, y)) -> 0 [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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [1]
   app(c_app(plus, 0), y) -> y [1]
   app(c_app(plus, c_app(c_app(plus, x), c_app(s, 0))), c_app(c_app(plus, y), c_app(s, c_app(s, z)))) -> app(app(plus, app(app(plus, y), app(s, app(s, z)))), app(app(plus, x), app(s, 0))) [1]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(plus) -> plus [0]
   encArg(map) -> map [0]
   encArg(nil) -> nil [0]
   encArg(cons) -> cons [0]
   encArg(filter) -> filter [0]
   encArg(filter2) -> filter2 [0]
   encArg(true) -> true [0]
   encArg(false) -> false [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_minus -> minus [0]
   encode_0 -> 0 [0]
   encode_s -> s [0]
   encode_quot -> quot [0]
   encode_plus -> plus [0]
   encode_map -> map [0]
   encode_nil -> nil [0]
   encode_cons -> cons [0]
   encode_filter -> filter [0]
   encode_filter2 -> filter2 [0]
   encode_true -> true [0]
   encode_false -> false [0]
   app(x0, x1) -> c_app(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_app(v0, v1) -> null_encode_app [0]
   encode_minus -> null_encode_minus [0]
   encode_0 -> null_encode_0 [0]
   encode_s -> null_encode_s [0]
   encode_quot -> null_encode_quot [0]
   encode_plus -> null_encode_plus [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]
   encode_true -> null_encode_true [0]
   encode_false -> null_encode_false [0]
   app(v0, v1) -> null_app [0]

The TRS has the following type information:
app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
c_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encArg :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_minus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_0 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_s :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_quot :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_plus :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_map :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_nil :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_cons :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_filter2 :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_true :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_encode_false :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
null_app :: map:c_app:cons:filter2:false:filter:nil:minus:0:plus:s:quot:true:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_plus:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false: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 => 5
   cons => 1
   filter2 => 4
   false => 2
   filter => 3
   nil => 7
   minus => 6
   0 => 0
   plus => 8
   s => 10
   quot => 9
   true => 11
   null_encArg => 0
   null_encode_app => 0
   null_encode_minus => 0
   null_encode_0 => 0
   null_encode_s => 0
   null_encode_quot => 0
   null_encode_plus => 0
   null_encode_map => 0
   null_encode_nil => 0
   null_encode_cons => 0
   null_encode_filter => 0
   null_encode_filter2 => 0
   null_encode_true => 0
   null_encode_false => 0
   null_app => 0

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

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

   app(z', z'') -{ 1 }-> x :|: z'' = 0, x >= 0, z' = 1 + 6 + x
   app(z', z'') -{ 1 }-> y :|: z' = 1 + 8 + 0, z'' = y, y >= 0
   app(z', z'') -{ 1 }-> app(app(app(app(4, app(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs, z' = 1 + 3 + f
   app(z', z'') -{ 1 }-> app(app(8, app(app(8, y), app(10, app(10, z)))), app(app(8, x), app(10, 0))) :|: z >= 0, z' = 1 + 8 + (1 + (1 + 8 + x) + (1 + 10 + 0)), x >= 0, y >= 0, z'' = 1 + (1 + 8 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(8, app(app(6, y), app(10, app(10, z)))), app(app(6, x), app(10, 0))) :|: z' = 1 + 8 + (1 + (1 + 6 + x) + (1 + 10 + 0)), z >= 0, x >= 0, y >= 0, z'' = 1 + (1 + 6 + y) + (1 + 10 + (1 + 10 + z))
   app(z', z'') -{ 1 }-> app(app(6, x), y) :|: z' = 1 + 6 + (1 + 10 + x), x >= 0, y >= 0, z'' = 1 + 10 + y
   app(z', z'') -{ 1 }-> app(app(3, f), xs) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 4 + 2) + f) + x
   app(z', z'') -{ 1 }-> app(app(1, x), app(app(3, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 4 + 11) + f) + x
   app(z', z'') -{ 1 }-> app(app(1, app(f, x)), app(app(5, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z' = 1 + 5 + f, z'' = 1 + (1 + 1 + x) + xs
   app(z', z'') -{ 1 }-> app(10, app(app(9, app(app(6, x), y)), app(10, y))) :|: x >= 0, y >= 0, z' = 1 + 9 + (1 + 10 + x), z'' = 1 + 10 + y
   app(z', z'') -{ 1 }-> app(10, app(app(8, x), y)) :|: z'' = y, x >= 0, y >= 0, z' = 1 + 8 + (1 + 10 + x)
   app(z', z'') -{ 1 }-> 7 :|: f >= 0, z'' = 7, z' = 1 + 5 + f
   app(z', z'') -{ 1 }-> 7 :|: f >= 0, z'' = 7, z' = 1 + 3 + f
   app(z', z'') -{ 1 }-> 0 :|: z' = 1 + 9 + 0, y >= 0, z'' = 1 + 10 + y
   app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   app(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0
   encArg(z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2
   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 }-> 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, z' = x_1, x_2 >= 0, z'' = x_2
   encode_app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 4 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 5 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 6 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 7 :|: 
   encode_nil -{ 0 }-> 0 :|: 
   encode_plus -{ 0 }-> 8 :|: 
   encode_plus -{ 0 }-> 0 :|: 
   encode_quot -{ 0 }-> 9 :|: 
   encode_quot -{ 0 }-> 0 :|: 
   encode_s -{ 0 }-> 10 :|: 
   encode_s -{ 0 }-> 0 :|: 
   encode_true -{ 0 }-> 11 :|: 
   encode_true -{ 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(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus) -> c
   ENCARG(0) -> c1
   ENCARG(s) -> c2
   ENCARG(quot) -> c3
   ENCARG(plus) -> c4
   ENCARG(map) -> c5
   ENCARG(nil) -> c6
   ENCARG(cons) -> c7
   ENCARG(filter) -> c8
   ENCARG(filter2) -> c9
   ENCARG(true) -> c10
   ENCARG(false) -> c11
   ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c13(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_MINUS -> c14
   ENCODE_0 -> c15
   ENCODE_S -> c16
   ENCODE_QUOT -> c17
   ENCODE_PLUS -> c18
   ENCODE_MAP -> c19
   ENCODE_NIL -> c20
   ENCODE_CONS -> c21
   ENCODE_FILTER -> c22
   ENCODE_FILTER2 -> c23
   ENCODE_TRUE -> c24
   ENCODE_FALSE -> c25
   APP(app(minus, z0), 0) -> c26
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1), APP(minus, z0))
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1))), APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(quot, app(app(minus, z0), z1)), APP(app(minus, z0), z1), APP(minus, z0), APP(s, z1))
   APP(app(plus, 0), z0) -> c30
   APP(app(plus, app(s, z0)), z1) -> c31(APP(s, app(app(plus, z0), z1)), APP(app(plus, z0), z1), APP(plus, z0))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c32(APP(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0))), APP(plus, app(app(minus, z1), app(s, app(s, z2)))), APP(app(minus, z1), app(s, app(s, z2))), APP(minus, z1), APP(s, app(s, z2)), APP(s, z2), APP(app(minus, z0), app(s, 0)), APP(minus, z0), APP(s, 0))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0))), APP(plus, app(app(plus, z1), app(s, app(s, z2)))), APP(app(plus, z1), app(s, app(s, z2))), APP(plus, z1), APP(s, app(s, z2)), APP(s, z2), APP(app(plus, z0), app(s, 0)), APP(plus, z0), APP(s, 0))
   APP(app(map, z0), nil) -> c34
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(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) -> c36
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(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) -> c38(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) -> c39(APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1), APP(minus, z0))
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1))), APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(quot, app(app(minus, z0), z1)), APP(app(minus, z0), z1), APP(minus, z0), APP(s, z1))
   APP(app(plus, 0), z0) -> c30
   APP(app(plus, app(s, z0)), z1) -> c31(APP(s, app(app(plus, z0), z1)), APP(app(plus, z0), z1), APP(plus, z0))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c32(APP(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0))), APP(plus, app(app(minus, z1), app(s, app(s, z2)))), APP(app(minus, z1), app(s, app(s, z2))), APP(minus, z1), APP(s, app(s, z2)), APP(s, z2), APP(app(minus, z0), app(s, 0)), APP(minus, z0), APP(s, 0))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0))), APP(plus, app(app(plus, z1), app(s, app(s, z2)))), APP(app(plus, z1), app(s, app(s, z2))), APP(plus, z1), APP(s, app(s, z2)), APP(s, z2), APP(app(plus, z0), app(s, 0)), APP(plus, z0), APP(s, 0))
   APP(app(map, z0), nil) -> c34
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(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) -> c36
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(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) -> c38(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) -> c39(APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_quot, encode_plus, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, ENCODE_MINUS, ENCODE_0, ENCODE_S, ENCODE_QUOT, ENCODE_PLUS, ENCODE_MAP, ENCODE_NIL, ENCODE_CONS, ENCODE_FILTER, ENCODE_FILTER2, ENCODE_TRUE, ENCODE_FALSE, APP_2

Compound Symbols:   c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12_3, c13_3, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27_2, c28, c29_6, c30, c31_3, c32_9, c33_9, c34, c35_5, c36, c37_5, c38_4, c39_2


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

(35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 24 trailing nodes:
   ENCODE_FILTER2 -> c23
   ENCARG(plus) -> c4
   ENCARG(false) -> c11
   ENCARG(cons) -> c7
   ENCARG(true) -> c10
   ENCARG(map) -> c5
   ENCODE_FALSE -> c25
   ENCODE_MAP -> c19
   ENCODE_CONS -> c21
   ENCARG(quot) -> c3
   ENCARG(minus) -> c
   ENCODE_NIL -> c20
   ENCARG(filter2) -> c9
   ENCODE_MINUS -> c14
   ENCARG(filter) -> c8
   ENCARG(nil) -> c6
   ENCODE_TRUE -> c24
   ENCODE_QUOT -> c17
   ENCARG(0) -> c1
   ENCODE_PLUS -> c18
   ENCARG(s) -> c2
   ENCODE_0 -> c15
   ENCODE_S -> c16
   ENCODE_FILTER -> c22

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c13(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(minus, z0), 0) -> c26
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1), APP(minus, z0))
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1))), APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(quot, app(app(minus, z0), z1)), APP(app(minus, z0), z1), APP(minus, z0), APP(s, z1))
   APP(app(plus, 0), z0) -> c30
   APP(app(plus, app(s, z0)), z1) -> c31(APP(s, app(app(plus, z0), z1)), APP(app(plus, z0), z1), APP(plus, z0))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c32(APP(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0))), APP(plus, app(app(minus, z1), app(s, app(s, z2)))), APP(app(minus, z1), app(s, app(s, z2))), APP(minus, z1), APP(s, app(s, z2)), APP(s, z2), APP(app(minus, z0), app(s, 0)), APP(minus, z0), APP(s, 0))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0))), APP(plus, app(app(plus, z1), app(s, app(s, z2)))), APP(app(plus, z1), app(s, app(s, z2))), APP(plus, z1), APP(s, app(s, z2)), APP(s, z2), APP(app(plus, z0), app(s, 0)), APP(plus, z0), APP(s, 0))
   APP(app(map, z0), nil) -> c34
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(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) -> c36
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(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) -> c38(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) -> c39(APP(app(filter, z0), z2), APP(filter, z0))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1), APP(minus, z0))
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1))), APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(quot, app(app(minus, z0), z1)), APP(app(minus, z0), z1), APP(minus, z0), APP(s, z1))
   APP(app(plus, 0), z0) -> c30
   APP(app(plus, app(s, z0)), z1) -> c31(APP(s, app(app(plus, z0), z1)), APP(app(plus, z0), z1), APP(plus, z0))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c32(APP(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0))), APP(plus, app(app(minus, z1), app(s, app(s, z2)))), APP(app(minus, z1), app(s, app(s, z2))), APP(minus, z1), APP(s, app(s, z2)), APP(s, z2), APP(app(minus, z0), app(s, 0)), APP(minus, z0), APP(s, 0))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0))), APP(plus, app(app(plus, z1), app(s, app(s, z2)))), APP(app(plus, z1), app(s, app(s, z2))), APP(plus, z1), APP(s, app(s, z2)), APP(s, z2), APP(app(plus, z0), app(s, 0)), APP(plus, z0), APP(s, 0))
   APP(app(map, z0), nil) -> c34
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(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) -> c36
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(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) -> c38(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) -> c39(APP(app(filter, z0), z2), APP(filter, z0))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_quot, encode_plus, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c12_3, c13_3, c26, c27_2, c28, c29_6, c30, c31_3, c32_9, c33_9, c34, c35_5, c36, c37_5, c38_4, c39_2


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

(37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 31 trailing tuple parts
----------------------------------------

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_APP(z0, z1) -> c13(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c32(APP(app(minus, z1), app(s, app(s, z2))), APP(app(minus, z0), app(s, 0)))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c32(APP(app(minus, z1), app(s, app(s, z2))), APP(app(minus, z0), app(s, 0)))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_quot, encode_plus, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false

Defined Pair Symbols:   ENCARG_1, ENCODE_APP_2, APP_2

Compound Symbols:   c12_3, c13_3, c26, c28, c30, c34, c36, c27_1, c29_2, c31_1, c32_2, c33_2, c35_2, c37_2, c38_1, c39_1


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

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(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))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_quot, encode_plus, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c12_3, c26, c28, c30, c34, c36, c27_1, c29_2, c31_1, c33_2, c35_2, c37_2, c38_1, c39_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(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   encode_app(z0, z1) -> app(encArg(z0), encArg(z1))
   encode_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
K tuples:none
Defined Rule Symbols:   app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_quot, encode_plus, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c12_3, c26, c28, c30, c34, c36, c27_1, c29_2, c31_1, c33_2, c35_2, c37_2, c38_1, c39_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_minus -> minus
   encode_0 -> 0
   encode_s -> s
   encode_quot -> quot
   encode_plus -> plus
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c12_3, c26, c28, c30, c34, c36, c27_1, c29_2, c31_1, c33_2, c35_2, c37_2, c38_1, c39_1, c_1


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

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0), ENCARG(minus))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0), ENCARG(s))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0), ENCARG(quot))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0), ENCARG(plus))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(minus, x1)) -> c12(APP(minus, encArg(x1)), ENCARG(minus), ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(APP(quot, encArg(x1)), ENCARG(quot), ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(APP(plus, encArg(x1)), ENCARG(plus), ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0), ENCARG(minus))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0), ENCARG(s))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0), ENCARG(quot))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0), ENCARG(plus))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0), ENCARG(map))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0), ENCARG(true))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0), ENCARG(false))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(minus, x1)) -> c12(APP(minus, encArg(x1)), ENCARG(minus), ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(APP(quot, encArg(x1)), ENCARG(quot), ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(APP(plus, encArg(x1)), ENCARG(plus), ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c29_2, c31_1, c33_2, c35_2, c37_2, c38_1, c39_1, c_1, c12_3


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

(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 36 trailing tuple parts
----------------------------------------

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c29_2, c31_1, c33_2, c35_2, c37_2, c38_1, c39_1, c_1, c12_3, c12_2, c12_1


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(quot, app(s, z0)), app(s, z1)) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, z1)), APP(app(minus, z0), z1)) by 
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, 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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c37_2, c38_1, c39_1, c_1, c12_3, c12_2, c12_1, c29_2


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c37(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) by 
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(app(app(filter2, 0), app(quot, 0)), app(s, z0)), x2), APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))), app(quot, app(s, z0))), app(s, z1)), x2), APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(app(app(filter2, app(s, app(app(plus, z0), z1))), app(plus, app(s, z0))), z1), x2), APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(app(app(filter2, app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))), app(plus, app(app(minus, z0), app(s, 0)))), app(app(minus, z1), app(s, app(s, z2)))), x2), APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(app(app(filter2, app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))), app(plus, app(app(plus, z0), app(s, 0)))), app(app(plus, z1), app(s, app(s, z2)))), x2), APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(app(app(filter2, 0), app(quot, 0)), app(s, z0)), x2), APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))), app(quot, app(s, z0))), app(s, z1)), x2), APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(app(app(filter2, app(s, app(app(plus, z0), z1))), app(plus, app(s, z0))), z1), x2), APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(app(app(filter2, app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))), app(plus, app(app(minus, z0), app(s, 0)))), app(app(minus, z1), app(s, app(s, z2)))), x2), APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(app(app(filter2, app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))), app(plus, app(app(plus, z0), app(s, 0)))), app(app(plus, z1), app(s, app(s, z2)))), x2), APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(app(app(filter2, 0), app(quot, 0)), app(s, z0)), x2), APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))), app(quot, app(s, z0))), app(s, z1)), x2), APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(app(app(filter2, app(s, app(app(plus, z0), z1))), app(plus, app(s, z0))), z1), x2), APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(app(app(filter2, app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))), app(plus, app(app(minus, z0), app(s, 0)))), app(app(minus, z1), app(s, app(s, z2)))), x2), APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(app(app(filter2, app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))), app(plus, app(app(plus, z0), app(s, 0)))), app(app(plus, z1), app(s, app(s, z2)))), x2), APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_3, c12_2, c12_1, c29_2, c37_2


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

(53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 9 trailing tuple parts
----------------------------------------

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_3, c12_2, c12_1, c29_2, c37_2, c37_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by 
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))
   ENCODE_APP(quot, x1) -> c(APP(quot, encArg(x1)))
   ENCODE_APP(plus, x1) -> c(APP(plus, 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(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1))))
   ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))
   ENCODE_APP(quot, x1) -> c(APP(quot, encArg(x1)))
   ENCODE_APP(plus, x1) -> c(APP(plus, 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(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_3, c12_2, c12_1, c29_2, c37_2, c37_1


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

(57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   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(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1)))
   ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(quot, x1) -> c(APP(quot, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(plus, x1) -> c(APP(plus, encArg(x1)))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_3, c12_2, c12_1, c29_2, c37_2, c37_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by 
   ENCARG(cons_app(x0, cons_app(x1, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(APP(minus, app(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(APP(quot, app(encArg(x1), encArg(x2))), ENCARG(quot), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(APP(plus, app(encArg(x1), encArg(x2))), ENCARG(plus), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(APP(minus, app(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(APP(quot, app(encArg(x1), encArg(x2))), ENCARG(quot), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(APP(plus, app(encArg(x1), encArg(x2))), ENCARG(plus), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c12(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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_3, c12_2, c12_1, c29_2, c37_2, c37_1


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

(61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 24 trailing tuple parts
----------------------------------------

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_3, c12_2, c12_1, c29_2, c37_2, c37_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)), ENCARG(minus))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)), ENCARG(quot))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)), ENCARG(plus))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c12(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, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c12(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, x1), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)), ENCARG(minus))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)), ENCARG(quot))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)), ENCARG(plus))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c12(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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 19 trailing tuple parts
----------------------------------------

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, minus)) -> c12(APP(encArg(x0), minus), ENCARG(x0)) by 
   ENCARG(cons_app(minus, minus)) -> c12(APP(minus, minus), ENCARG(minus))
   ENCARG(cons_app(0, minus)) -> c12(APP(0, minus), ENCARG(0))
   ENCARG(cons_app(s, minus)) -> c12(APP(s, minus), ENCARG(s))
   ENCARG(cons_app(quot, minus)) -> c12(APP(quot, minus), ENCARG(quot))
   ENCARG(cons_app(plus, minus)) -> c12(APP(plus, minus), ENCARG(plus))
   ENCARG(cons_app(map, minus)) -> c12(APP(map, minus), ENCARG(map))
   ENCARG(cons_app(nil, minus)) -> c12(APP(nil, minus), ENCARG(nil))
   ENCARG(cons_app(cons, minus)) -> c12(APP(cons, minus), ENCARG(cons))
   ENCARG(cons_app(filter, minus)) -> c12(APP(filter, minus), ENCARG(filter))
   ENCARG(cons_app(filter2, minus)) -> c12(APP(filter2, minus), ENCARG(filter2))
   ENCARG(cons_app(true, minus)) -> c12(APP(true, minus), ENCARG(true))
   ENCARG(cons_app(false, minus)) -> c12(APP(false, minus), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), minus)) -> c12(APP(app(encArg(z0), encArg(z1)), minus), ENCARG(cons_app(z0, z1)))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, minus)) -> c12(APP(minus, minus), ENCARG(minus))
   ENCARG(cons_app(0, minus)) -> c12(APP(0, minus), ENCARG(0))
   ENCARG(cons_app(s, minus)) -> c12(APP(s, minus), ENCARG(s))
   ENCARG(cons_app(quot, minus)) -> c12(APP(quot, minus), ENCARG(quot))
   ENCARG(cons_app(plus, minus)) -> c12(APP(plus, minus), ENCARG(plus))
   ENCARG(cons_app(map, minus)) -> c12(APP(map, minus), ENCARG(map))
   ENCARG(cons_app(nil, minus)) -> c12(APP(nil, minus), ENCARG(nil))
   ENCARG(cons_app(cons, minus)) -> c12(APP(cons, minus), ENCARG(cons))
   ENCARG(cons_app(filter, minus)) -> c12(APP(filter, minus), ENCARG(filter))
   ENCARG(cons_app(filter2, minus)) -> c12(APP(filter2, minus), ENCARG(filter2))
   ENCARG(cons_app(true, minus)) -> c12(APP(true, minus), ENCARG(true))
   ENCARG(cons_app(false, minus)) -> c12(APP(false, minus), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(filter2, minus)) -> c12(APP(filter2, minus), ENCARG(filter2))
   ENCARG(cons_app(s, minus)) -> c12(APP(s, minus), ENCARG(s))
   ENCARG(cons_app(nil, minus)) -> c12(APP(nil, minus), ENCARG(nil))
   ENCARG(cons_app(false, minus)) -> c12(APP(false, minus), ENCARG(false))
   ENCARG(cons_app(map, minus)) -> c12(APP(map, minus), ENCARG(map))
   ENCARG(cons_app(filter, minus)) -> c12(APP(filter, minus), ENCARG(filter))
   ENCARG(cons_app(true, minus)) -> c12(APP(true, minus), ENCARG(true))
   ENCARG(cons_app(cons, minus)) -> c12(APP(cons, minus), ENCARG(cons))
   ENCARG(cons_app(quot, minus)) -> c12(APP(quot, minus), ENCARG(quot))
   ENCARG(cons_app(plus, minus)) -> c12(APP(plus, minus), ENCARG(plus))
   ENCARG(cons_app(minus, minus)) -> c12(APP(minus, minus), ENCARG(minus))
   ENCARG(cons_app(0, minus)) -> c12(APP(0, minus), ENCARG(0))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) by 
   ENCARG(cons_app(minus, 0)) -> c12(APP(minus, 0), ENCARG(minus))
   ENCARG(cons_app(0, 0)) -> c12(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(s, 0)) -> c12(APP(s, 0), ENCARG(s))
   ENCARG(cons_app(quot, 0)) -> c12(APP(quot, 0), ENCARG(quot))
   ENCARG(cons_app(plus, 0)) -> c12(APP(plus, 0), ENCARG(plus))
   ENCARG(cons_app(map, 0)) -> c12(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(nil, 0)) -> c12(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(cons, 0)) -> c12(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(filter, 0)) -> c12(APP(filter, 0), ENCARG(filter))
   ENCARG(cons_app(filter2, 0)) -> c12(APP(filter2, 0), ENCARG(filter2))
   ENCARG(cons_app(true, 0)) -> c12(APP(true, 0), ENCARG(true))
   ENCARG(cons_app(false, 0)) -> c12(APP(false, 0), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), 0)) -> c12(APP(app(encArg(z0), encArg(z1)), 0), ENCARG(cons_app(z0, z1)))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, 0)) -> c12(APP(minus, 0), ENCARG(minus))
   ENCARG(cons_app(0, 0)) -> c12(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(s, 0)) -> c12(APP(s, 0), ENCARG(s))
   ENCARG(cons_app(quot, 0)) -> c12(APP(quot, 0), ENCARG(quot))
   ENCARG(cons_app(plus, 0)) -> c12(APP(plus, 0), ENCARG(plus))
   ENCARG(cons_app(map, 0)) -> c12(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(nil, 0)) -> c12(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(cons, 0)) -> c12(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(filter, 0)) -> c12(APP(filter, 0), ENCARG(filter))
   ENCARG(cons_app(filter2, 0)) -> c12(APP(filter2, 0), ENCARG(filter2))
   ENCARG(cons_app(true, 0)) -> c12(APP(true, 0), ENCARG(true))
   ENCARG(cons_app(false, 0)) -> c12(APP(false, 0), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(cons, 0)) -> c12(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(plus, 0)) -> c12(APP(plus, 0), ENCARG(plus))
   ENCARG(cons_app(quot, 0)) -> c12(APP(quot, 0), ENCARG(quot))
   ENCARG(cons_app(false, 0)) -> c12(APP(false, 0), ENCARG(false))
   ENCARG(cons_app(true, 0)) -> c12(APP(true, 0), ENCARG(true))
   ENCARG(cons_app(nil, 0)) -> c12(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(s, 0)) -> c12(APP(s, 0), ENCARG(s))
   ENCARG(cons_app(0, 0)) -> c12(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(filter, 0)) -> c12(APP(filter, 0), ENCARG(filter))
   ENCARG(cons_app(filter2, 0)) -> c12(APP(filter2, 0), ENCARG(filter2))
   ENCARG(cons_app(minus, 0)) -> c12(APP(minus, 0), ENCARG(minus))
   ENCARG(cons_app(map, 0)) -> c12(APP(map, 0), ENCARG(map))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) by 
   ENCARG(cons_app(minus, s)) -> c12(APP(minus, s), ENCARG(minus))
   ENCARG(cons_app(0, s)) -> c12(APP(0, s), ENCARG(0))
   ENCARG(cons_app(s, s)) -> c12(APP(s, s), ENCARG(s))
   ENCARG(cons_app(quot, s)) -> c12(APP(quot, s), ENCARG(quot))
   ENCARG(cons_app(plus, s)) -> c12(APP(plus, s), ENCARG(plus))
   ENCARG(cons_app(map, s)) -> c12(APP(map, s), ENCARG(map))
   ENCARG(cons_app(nil, s)) -> c12(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(cons, s)) -> c12(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(filter, s)) -> c12(APP(filter, s), ENCARG(filter))
   ENCARG(cons_app(filter2, s)) -> c12(APP(filter2, s), ENCARG(filter2))
   ENCARG(cons_app(true, s)) -> c12(APP(true, s), ENCARG(true))
   ENCARG(cons_app(false, s)) -> c12(APP(false, s), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), s)) -> c12(APP(app(encArg(z0), encArg(z1)), s), ENCARG(cons_app(z0, z1)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, s)) -> c12(APP(minus, s), ENCARG(minus))
   ENCARG(cons_app(0, s)) -> c12(APP(0, s), ENCARG(0))
   ENCARG(cons_app(s, s)) -> c12(APP(s, s), ENCARG(s))
   ENCARG(cons_app(quot, s)) -> c12(APP(quot, s), ENCARG(quot))
   ENCARG(cons_app(plus, s)) -> c12(APP(plus, s), ENCARG(plus))
   ENCARG(cons_app(map, s)) -> c12(APP(map, s), ENCARG(map))
   ENCARG(cons_app(nil, s)) -> c12(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(cons, s)) -> c12(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(filter, s)) -> c12(APP(filter, s), ENCARG(filter))
   ENCARG(cons_app(filter2, s)) -> c12(APP(filter2, s), ENCARG(filter2))
   ENCARG(cons_app(true, s)) -> c12(APP(true, s), ENCARG(true))
   ENCARG(cons_app(false, s)) -> c12(APP(false, s), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(cons, s)) -> c12(APP(cons, s), ENCARG(cons))
   ENCARG(cons_app(quot, s)) -> c12(APP(quot, s), ENCARG(quot))
   ENCARG(cons_app(minus, s)) -> c12(APP(minus, s), ENCARG(minus))
   ENCARG(cons_app(nil, s)) -> c12(APP(nil, s), ENCARG(nil))
   ENCARG(cons_app(plus, s)) -> c12(APP(plus, s), ENCARG(plus))
   ENCARG(cons_app(0, s)) -> c12(APP(0, s), ENCARG(0))
   ENCARG(cons_app(false, s)) -> c12(APP(false, s), ENCARG(false))
   ENCARG(cons_app(filter2, s)) -> c12(APP(filter2, s), ENCARG(filter2))
   ENCARG(cons_app(s, s)) -> c12(APP(s, s), ENCARG(s))
   ENCARG(cons_app(map, s)) -> c12(APP(map, s), ENCARG(map))
   ENCARG(cons_app(filter, s)) -> c12(APP(filter, s), ENCARG(filter))
   ENCARG(cons_app(true, s)) -> c12(APP(true, s), ENCARG(true))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0)) by 
   ENCARG(cons_app(minus, quot)) -> c12(APP(minus, quot), ENCARG(minus))
   ENCARG(cons_app(0, quot)) -> c12(APP(0, quot), ENCARG(0))
   ENCARG(cons_app(s, quot)) -> c12(APP(s, quot), ENCARG(s))
   ENCARG(cons_app(quot, quot)) -> c12(APP(quot, quot), ENCARG(quot))
   ENCARG(cons_app(plus, quot)) -> c12(APP(plus, quot), ENCARG(plus))
   ENCARG(cons_app(map, quot)) -> c12(APP(map, quot), ENCARG(map))
   ENCARG(cons_app(nil, quot)) -> c12(APP(nil, quot), ENCARG(nil))
   ENCARG(cons_app(cons, quot)) -> c12(APP(cons, quot), ENCARG(cons))
   ENCARG(cons_app(filter, quot)) -> c12(APP(filter, quot), ENCARG(filter))
   ENCARG(cons_app(filter2, quot)) -> c12(APP(filter2, quot), ENCARG(filter2))
   ENCARG(cons_app(true, quot)) -> c12(APP(true, quot), ENCARG(true))
   ENCARG(cons_app(false, quot)) -> c12(APP(false, quot), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), quot)) -> c12(APP(app(encArg(z0), encArg(z1)), quot), ENCARG(cons_app(z0, z1)))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, quot)) -> c12(APP(minus, quot), ENCARG(minus))
   ENCARG(cons_app(0, quot)) -> c12(APP(0, quot), ENCARG(0))
   ENCARG(cons_app(s, quot)) -> c12(APP(s, quot), ENCARG(s))
   ENCARG(cons_app(quot, quot)) -> c12(APP(quot, quot), ENCARG(quot))
   ENCARG(cons_app(plus, quot)) -> c12(APP(plus, quot), ENCARG(plus))
   ENCARG(cons_app(map, quot)) -> c12(APP(map, quot), ENCARG(map))
   ENCARG(cons_app(nil, quot)) -> c12(APP(nil, quot), ENCARG(nil))
   ENCARG(cons_app(cons, quot)) -> c12(APP(cons, quot), ENCARG(cons))
   ENCARG(cons_app(filter, quot)) -> c12(APP(filter, quot), ENCARG(filter))
   ENCARG(cons_app(filter2, quot)) -> c12(APP(filter2, quot), ENCARG(filter2))
   ENCARG(cons_app(true, quot)) -> c12(APP(true, quot), ENCARG(true))
   ENCARG(cons_app(false, quot)) -> c12(APP(false, quot), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(false, quot)) -> c12(APP(false, quot), ENCARG(false))
   ENCARG(cons_app(filter, quot)) -> c12(APP(filter, quot), ENCARG(filter))
   ENCARG(cons_app(plus, quot)) -> c12(APP(plus, quot), ENCARG(plus))
   ENCARG(cons_app(minus, quot)) -> c12(APP(minus, quot), ENCARG(minus))
   ENCARG(cons_app(true, quot)) -> c12(APP(true, quot), ENCARG(true))
   ENCARG(cons_app(cons, quot)) -> c12(APP(cons, quot), ENCARG(cons))
   ENCARG(cons_app(quot, quot)) -> c12(APP(quot, quot), ENCARG(quot))
   ENCARG(cons_app(map, quot)) -> c12(APP(map, quot), ENCARG(map))
   ENCARG(cons_app(s, quot)) -> c12(APP(s, quot), ENCARG(s))
   ENCARG(cons_app(0, quot)) -> c12(APP(0, quot), ENCARG(0))
   ENCARG(cons_app(filter2, quot)) -> c12(APP(filter2, quot), ENCARG(filter2))
   ENCARG(cons_app(nil, quot)) -> c12(APP(nil, quot), ENCARG(nil))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, plus)) -> c12(APP(encArg(x0), plus), ENCARG(x0)) by 
   ENCARG(cons_app(minus, plus)) -> c12(APP(minus, plus), ENCARG(minus))
   ENCARG(cons_app(0, plus)) -> c12(APP(0, plus), ENCARG(0))
   ENCARG(cons_app(s, plus)) -> c12(APP(s, plus), ENCARG(s))
   ENCARG(cons_app(quot, plus)) -> c12(APP(quot, plus), ENCARG(quot))
   ENCARG(cons_app(plus, plus)) -> c12(APP(plus, plus), ENCARG(plus))
   ENCARG(cons_app(map, plus)) -> c12(APP(map, plus), ENCARG(map))
   ENCARG(cons_app(nil, plus)) -> c12(APP(nil, plus), ENCARG(nil))
   ENCARG(cons_app(cons, plus)) -> c12(APP(cons, plus), ENCARG(cons))
   ENCARG(cons_app(filter, plus)) -> c12(APP(filter, plus), ENCARG(filter))
   ENCARG(cons_app(filter2, plus)) -> c12(APP(filter2, plus), ENCARG(filter2))
   ENCARG(cons_app(true, plus)) -> c12(APP(true, plus), ENCARG(true))
   ENCARG(cons_app(false, plus)) -> c12(APP(false, plus), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), plus)) -> c12(APP(app(encArg(z0), encArg(z1)), plus), ENCARG(cons_app(z0, z1)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, plus)) -> c12(APP(minus, plus), ENCARG(minus))
   ENCARG(cons_app(0, plus)) -> c12(APP(0, plus), ENCARG(0))
   ENCARG(cons_app(s, plus)) -> c12(APP(s, plus), ENCARG(s))
   ENCARG(cons_app(quot, plus)) -> c12(APP(quot, plus), ENCARG(quot))
   ENCARG(cons_app(plus, plus)) -> c12(APP(plus, plus), ENCARG(plus))
   ENCARG(cons_app(map, plus)) -> c12(APP(map, plus), ENCARG(map))
   ENCARG(cons_app(nil, plus)) -> c12(APP(nil, plus), ENCARG(nil))
   ENCARG(cons_app(cons, plus)) -> c12(APP(cons, plus), ENCARG(cons))
   ENCARG(cons_app(filter, plus)) -> c12(APP(filter, plus), ENCARG(filter))
   ENCARG(cons_app(filter2, plus)) -> c12(APP(filter2, plus), ENCARG(filter2))
   ENCARG(cons_app(true, plus)) -> c12(APP(true, plus), ENCARG(true))
   ENCARG(cons_app(false, plus)) -> c12(APP(false, plus), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(minus, plus)) -> c12(APP(minus, plus), ENCARG(minus))
   ENCARG(cons_app(filter, plus)) -> c12(APP(filter, plus), ENCARG(filter))
   ENCARG(cons_app(filter2, plus)) -> c12(APP(filter2, plus), ENCARG(filter2))
   ENCARG(cons_app(nil, plus)) -> c12(APP(nil, plus), ENCARG(nil))
   ENCARG(cons_app(s, plus)) -> c12(APP(s, plus), ENCARG(s))
   ENCARG(cons_app(false, plus)) -> c12(APP(false, plus), ENCARG(false))
   ENCARG(cons_app(true, plus)) -> c12(APP(true, plus), ENCARG(true))
   ENCARG(cons_app(cons, plus)) -> c12(APP(cons, plus), ENCARG(cons))
   ENCARG(cons_app(quot, plus)) -> c12(APP(quot, plus), ENCARG(quot))
   ENCARG(cons_app(map, plus)) -> c12(APP(map, plus), ENCARG(map))
   ENCARG(cons_app(0, plus)) -> c12(APP(0, plus), ENCARG(0))
   ENCARG(cons_app(plus, plus)) -> c12(APP(plus, plus), ENCARG(plus))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, map)) -> c12(APP(encArg(x0), map), ENCARG(x0)) by 
   ENCARG(cons_app(minus, map)) -> c12(APP(minus, map), ENCARG(minus))
   ENCARG(cons_app(0, map)) -> c12(APP(0, map), ENCARG(0))
   ENCARG(cons_app(s, map)) -> c12(APP(s, map), ENCARG(s))
   ENCARG(cons_app(quot, map)) -> c12(APP(quot, map), ENCARG(quot))
   ENCARG(cons_app(plus, map)) -> c12(APP(plus, map), ENCARG(plus))
   ENCARG(cons_app(map, map)) -> c12(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c12(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c12(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(filter, map)) -> c12(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(filter2, map)) -> c12(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(true, map)) -> c12(APP(true, map), ENCARG(true))
   ENCARG(cons_app(false, map)) -> c12(APP(false, map), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), map)) -> c12(APP(app(encArg(z0), encArg(z1)), map), ENCARG(cons_app(z0, z1)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, map)) -> c12(APP(minus, map), ENCARG(minus))
   ENCARG(cons_app(0, map)) -> c12(APP(0, map), ENCARG(0))
   ENCARG(cons_app(s, map)) -> c12(APP(s, map), ENCARG(s))
   ENCARG(cons_app(quot, map)) -> c12(APP(quot, map), ENCARG(quot))
   ENCARG(cons_app(plus, map)) -> c12(APP(plus, map), ENCARG(plus))
   ENCARG(cons_app(map, map)) -> c12(APP(map, map), ENCARG(map))
   ENCARG(cons_app(nil, map)) -> c12(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(cons, map)) -> c12(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(filter, map)) -> c12(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(filter2, map)) -> c12(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(true, map)) -> c12(APP(true, map), ENCARG(true))
   ENCARG(cons_app(false, map)) -> c12(APP(false, map), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(true, map)) -> c12(APP(true, map), ENCARG(true))
   ENCARG(cons_app(minus, map)) -> c12(APP(minus, map), ENCARG(minus))
   ENCARG(cons_app(nil, map)) -> c12(APP(nil, map), ENCARG(nil))
   ENCARG(cons_app(plus, map)) -> c12(APP(plus, map), ENCARG(plus))
   ENCARG(cons_app(filter2, map)) -> c12(APP(filter2, map), ENCARG(filter2))
   ENCARG(cons_app(filter, map)) -> c12(APP(filter, map), ENCARG(filter))
   ENCARG(cons_app(map, map)) -> c12(APP(map, map), ENCARG(map))
   ENCARG(cons_app(cons, map)) -> c12(APP(cons, map), ENCARG(cons))
   ENCARG(cons_app(quot, map)) -> c12(APP(quot, map), ENCARG(quot))
   ENCARG(cons_app(s, map)) -> c12(APP(s, map), ENCARG(s))
   ENCARG(cons_app(0, map)) -> c12(APP(0, map), ENCARG(0))
   ENCARG(cons_app(false, map)) -> c12(APP(false, map), ENCARG(false))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) by 
   ENCARG(cons_app(minus, nil)) -> c12(APP(minus, nil), ENCARG(minus))
   ENCARG(cons_app(0, nil)) -> c12(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(s, nil)) -> c12(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(quot, nil)) -> c12(APP(quot, nil), ENCARG(quot))
   ENCARG(cons_app(plus, nil)) -> c12(APP(plus, nil), ENCARG(plus))
   ENCARG(cons_app(map, nil)) -> c12(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c12(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c12(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(filter, nil)) -> c12(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(filter2, nil)) -> c12(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(true, nil)) -> c12(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(false, nil)) -> c12(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), nil)) -> c12(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1)))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, nil)) -> c12(APP(minus, nil), ENCARG(minus))
   ENCARG(cons_app(0, nil)) -> c12(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(s, nil)) -> c12(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(quot, nil)) -> c12(APP(quot, nil), ENCARG(quot))
   ENCARG(cons_app(plus, nil)) -> c12(APP(plus, nil), ENCARG(plus))
   ENCARG(cons_app(map, nil)) -> c12(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(nil, nil)) -> c12(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(cons, nil)) -> c12(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(filter, nil)) -> c12(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(filter2, nil)) -> c12(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(true, nil)) -> c12(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(false, nil)) -> c12(APP(false, nil), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(cons, nil)) -> c12(APP(cons, nil), ENCARG(cons))
   ENCARG(cons_app(quot, nil)) -> c12(APP(quot, nil), ENCARG(quot))
   ENCARG(cons_app(plus, nil)) -> c12(APP(plus, nil), ENCARG(plus))
   ENCARG(cons_app(true, nil)) -> c12(APP(true, nil), ENCARG(true))
   ENCARG(cons_app(s, nil)) -> c12(APP(s, nil), ENCARG(s))
   ENCARG(cons_app(filter, nil)) -> c12(APP(filter, nil), ENCARG(filter))
   ENCARG(cons_app(0, nil)) -> c12(APP(0, nil), ENCARG(0))
   ENCARG(cons_app(map, nil)) -> c12(APP(map, nil), ENCARG(map))
   ENCARG(cons_app(false, nil)) -> c12(APP(false, nil), ENCARG(false))
   ENCARG(cons_app(filter2, nil)) -> c12(APP(filter2, nil), ENCARG(filter2))
   ENCARG(cons_app(nil, nil)) -> c12(APP(nil, nil), ENCARG(nil))
   ENCARG(cons_app(minus, nil)) -> c12(APP(minus, nil), ENCARG(minus))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) by 
   ENCARG(cons_app(minus, cons)) -> c12(APP(minus, cons), ENCARG(minus))
   ENCARG(cons_app(0, cons)) -> c12(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(s, cons)) -> c12(APP(s, cons), ENCARG(s))
   ENCARG(cons_app(quot, cons)) -> c12(APP(quot, cons), ENCARG(quot))
   ENCARG(cons_app(plus, cons)) -> c12(APP(plus, cons), ENCARG(plus))
   ENCARG(cons_app(map, cons)) -> c12(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c12(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c12(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(filter, cons)) -> c12(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(filter2, cons)) -> c12(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(true, cons)) -> c12(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c12(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), cons)) -> c12(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1)))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, cons)) -> c12(APP(minus, cons), ENCARG(minus))
   ENCARG(cons_app(0, cons)) -> c12(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(s, cons)) -> c12(APP(s, cons), ENCARG(s))
   ENCARG(cons_app(quot, cons)) -> c12(APP(quot, cons), ENCARG(quot))
   ENCARG(cons_app(plus, cons)) -> c12(APP(plus, cons), ENCARG(plus))
   ENCARG(cons_app(map, cons)) -> c12(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(nil, cons)) -> c12(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(cons, cons)) -> c12(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(filter, cons)) -> c12(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(filter2, cons)) -> c12(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(true, cons)) -> c12(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(false, cons)) -> c12(APP(false, cons), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(false, cons)) -> c12(APP(false, cons), ENCARG(false))
   ENCARG(cons_app(nil, cons)) -> c12(APP(nil, cons), ENCARG(nil))
   ENCARG(cons_app(minus, cons)) -> c12(APP(minus, cons), ENCARG(minus))
   ENCARG(cons_app(filter2, cons)) -> c12(APP(filter2, cons), ENCARG(filter2))
   ENCARG(cons_app(filter, cons)) -> c12(APP(filter, cons), ENCARG(filter))
   ENCARG(cons_app(true, cons)) -> c12(APP(true, cons), ENCARG(true))
   ENCARG(cons_app(0, cons)) -> c12(APP(0, cons), ENCARG(0))
   ENCARG(cons_app(map, cons)) -> c12(APP(map, cons), ENCARG(map))
   ENCARG(cons_app(plus, cons)) -> c12(APP(plus, cons), ENCARG(plus))
   ENCARG(cons_app(cons, cons)) -> c12(APP(cons, cons), ENCARG(cons))
   ENCARG(cons_app(quot, cons)) -> c12(APP(quot, cons), ENCARG(quot))
   ENCARG(cons_app(s, cons)) -> c12(APP(s, cons), ENCARG(s))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) by 
   ENCARG(cons_app(minus, filter)) -> c12(APP(minus, filter), ENCARG(minus))
   ENCARG(cons_app(0, filter)) -> c12(APP(0, filter), ENCARG(0))
   ENCARG(cons_app(s, filter)) -> c12(APP(s, filter), ENCARG(s))
   ENCARG(cons_app(quot, filter)) -> c12(APP(quot, filter), ENCARG(quot))
   ENCARG(cons_app(plus, filter)) -> c12(APP(plus, filter), ENCARG(plus))
   ENCARG(cons_app(map, filter)) -> c12(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(nil, filter)) -> c12(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons, filter)) -> c12(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c12(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(filter2, filter)) -> c12(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(true, filter)) -> c12(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(false, filter)) -> c12(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), filter)) -> c12(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1)))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, filter)) -> c12(APP(minus, filter), ENCARG(minus))
   ENCARG(cons_app(0, filter)) -> c12(APP(0, filter), ENCARG(0))
   ENCARG(cons_app(s, filter)) -> c12(APP(s, filter), ENCARG(s))
   ENCARG(cons_app(quot, filter)) -> c12(APP(quot, filter), ENCARG(quot))
   ENCARG(cons_app(plus, filter)) -> c12(APP(plus, filter), ENCARG(plus))
   ENCARG(cons_app(map, filter)) -> c12(APP(map, filter), ENCARG(map))
   ENCARG(cons_app(nil, filter)) -> c12(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(cons, filter)) -> c12(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(filter, filter)) -> c12(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(filter2, filter)) -> c12(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(true, filter)) -> c12(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(false, filter)) -> c12(APP(false, filter), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(nil, filter)) -> c12(APP(nil, filter), ENCARG(nil))
   ENCARG(cons_app(plus, filter)) -> c12(APP(plus, filter), ENCARG(plus))
   ENCARG(cons_app(false, filter)) -> c12(APP(false, filter), ENCARG(false))
   ENCARG(cons_app(true, filter)) -> c12(APP(true, filter), ENCARG(true))
   ENCARG(cons_app(cons, filter)) -> c12(APP(cons, filter), ENCARG(cons))
   ENCARG(cons_app(quot, filter)) -> c12(APP(quot, filter), ENCARG(quot))
   ENCARG(cons_app(0, filter)) -> c12(APP(0, filter), ENCARG(0))
   ENCARG(cons_app(minus, filter)) -> c12(APP(minus, filter), ENCARG(minus))
   ENCARG(cons_app(filter2, filter)) -> c12(APP(filter2, filter), ENCARG(filter2))
   ENCARG(cons_app(s, filter)) -> c12(APP(s, filter), ENCARG(s))
   ENCARG(cons_app(filter, filter)) -> c12(APP(filter, filter), ENCARG(filter))
   ENCARG(cons_app(map, filter)) -> c12(APP(map, filter), ENCARG(map))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, filter2)) -> c12(APP(encArg(x0), filter2), ENCARG(x0)) by 
   ENCARG(cons_app(minus, filter2)) -> c12(APP(minus, filter2), ENCARG(minus))
   ENCARG(cons_app(0, filter2)) -> c12(APP(0, filter2), ENCARG(0))
   ENCARG(cons_app(s, filter2)) -> c12(APP(s, filter2), ENCARG(s))
   ENCARG(cons_app(quot, filter2)) -> c12(APP(quot, filter2), ENCARG(quot))
   ENCARG(cons_app(plus, filter2)) -> c12(APP(plus, filter2), ENCARG(plus))
   ENCARG(cons_app(map, filter2)) -> c12(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(nil, filter2)) -> c12(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(cons, filter2)) -> c12(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(filter, filter2)) -> c12(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(filter2, filter2)) -> c12(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(true, filter2)) -> c12(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(false, filter2)) -> c12(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), filter2)) -> c12(APP(app(encArg(z0), encArg(z1)), filter2), ENCARG(cons_app(z0, z1)))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, filter2)) -> c12(APP(minus, filter2), ENCARG(minus))
   ENCARG(cons_app(0, filter2)) -> c12(APP(0, filter2), ENCARG(0))
   ENCARG(cons_app(s, filter2)) -> c12(APP(s, filter2), ENCARG(s))
   ENCARG(cons_app(quot, filter2)) -> c12(APP(quot, filter2), ENCARG(quot))
   ENCARG(cons_app(plus, filter2)) -> c12(APP(plus, filter2), ENCARG(plus))
   ENCARG(cons_app(map, filter2)) -> c12(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(nil, filter2)) -> c12(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(cons, filter2)) -> c12(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(filter, filter2)) -> c12(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(filter2, filter2)) -> c12(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(true, filter2)) -> c12(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(false, filter2)) -> c12(APP(false, filter2), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(minus, filter2)) -> c12(APP(minus, filter2), ENCARG(minus))
   ENCARG(cons_app(cons, filter2)) -> c12(APP(cons, filter2), ENCARG(cons))
   ENCARG(cons_app(quot, filter2)) -> c12(APP(quot, filter2), ENCARG(quot))
   ENCARG(cons_app(nil, filter2)) -> c12(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(false, filter2)) -> c12(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(true, filter2)) -> c12(APP(true, filter2), ENCARG(true))
   ENCARG(cons_app(filter, filter2)) -> c12(APP(filter, filter2), ENCARG(filter))
   ENCARG(cons_app(map, filter2)) -> c12(APP(map, filter2), ENCARG(map))
   ENCARG(cons_app(0, filter2)) -> c12(APP(0, filter2), ENCARG(0))
   ENCARG(cons_app(s, filter2)) -> c12(APP(s, filter2), ENCARG(s))
   ENCARG(cons_app(plus, filter2)) -> c12(APP(plus, filter2), ENCARG(plus))
   ENCARG(cons_app(filter2, filter2)) -> c12(APP(filter2, filter2), ENCARG(filter2))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) by 
   ENCARG(cons_app(minus, true)) -> c12(APP(minus, true), ENCARG(minus))
   ENCARG(cons_app(0, true)) -> c12(APP(0, true), ENCARG(0))
   ENCARG(cons_app(s, true)) -> c12(APP(s, true), ENCARG(s))
   ENCARG(cons_app(quot, true)) -> c12(APP(quot, true), ENCARG(quot))
   ENCARG(cons_app(plus, true)) -> c12(APP(plus, true), ENCARG(plus))
   ENCARG(cons_app(map, true)) -> c12(APP(map, true), ENCARG(map))
   ENCARG(cons_app(nil, true)) -> c12(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c12(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c12(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(filter2, true)) -> c12(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(true, true)) -> c12(APP(true, true), ENCARG(true))
   ENCARG(cons_app(false, true)) -> c12(APP(false, true), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), true)) -> c12(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1)))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, true)) -> c12(APP(minus, true), ENCARG(minus))
   ENCARG(cons_app(0, true)) -> c12(APP(0, true), ENCARG(0))
   ENCARG(cons_app(s, true)) -> c12(APP(s, true), ENCARG(s))
   ENCARG(cons_app(quot, true)) -> c12(APP(quot, true), ENCARG(quot))
   ENCARG(cons_app(plus, true)) -> c12(APP(plus, true), ENCARG(plus))
   ENCARG(cons_app(map, true)) -> c12(APP(map, true), ENCARG(map))
   ENCARG(cons_app(nil, true)) -> c12(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(cons, true)) -> c12(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(filter, true)) -> c12(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(filter2, true)) -> c12(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(true, true)) -> c12(APP(true, true), ENCARG(true))
   ENCARG(cons_app(false, true)) -> c12(APP(false, true), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(map, true)) -> c12(APP(map, true), ENCARG(map))
   ENCARG(cons_app(plus, true)) -> c12(APP(plus, true), ENCARG(plus))
   ENCARG(cons_app(s, true)) -> c12(APP(s, true), ENCARG(s))
   ENCARG(cons_app(cons, true)) -> c12(APP(cons, true), ENCARG(cons))
   ENCARG(cons_app(quot, true)) -> c12(APP(quot, true), ENCARG(quot))
   ENCARG(cons_app(filter2, true)) -> c12(APP(filter2, true), ENCARG(filter2))
   ENCARG(cons_app(filter, true)) -> c12(APP(filter, true), ENCARG(filter))
   ENCARG(cons_app(true, true)) -> c12(APP(true, true), ENCARG(true))
   ENCARG(cons_app(0, true)) -> c12(APP(0, true), ENCARG(0))
   ENCARG(cons_app(minus, true)) -> c12(APP(minus, true), ENCARG(minus))
   ENCARG(cons_app(nil, true)) -> c12(APP(nil, true), ENCARG(nil))
   ENCARG(cons_app(false, true)) -> c12(APP(false, true), ENCARG(false))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_2, c12_1, c29_2, c37_2, c37_1, c12_3


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) by 
   ENCARG(cons_app(minus, false)) -> c12(APP(minus, false), ENCARG(minus))
   ENCARG(cons_app(0, false)) -> c12(APP(0, false), ENCARG(0))
   ENCARG(cons_app(s, false)) -> c12(APP(s, false), ENCARG(s))
   ENCARG(cons_app(quot, false)) -> c12(APP(quot, false), ENCARG(quot))
   ENCARG(cons_app(plus, false)) -> c12(APP(plus, false), ENCARG(plus))
   ENCARG(cons_app(map, false)) -> c12(APP(map, false), ENCARG(map))
   ENCARG(cons_app(nil, false)) -> c12(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c12(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(filter, false)) -> c12(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(filter2, false)) -> c12(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(true, false)) -> c12(APP(true, false), ENCARG(true))
   ENCARG(cons_app(false, false)) -> c12(APP(false, false), ENCARG(false))
   ENCARG(cons_app(cons_app(z0, z1), false)) -> c12(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1)))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   ENCARG(cons_app(minus, false)) -> c12(APP(minus, false), ENCARG(minus))
   ENCARG(cons_app(0, false)) -> c12(APP(0, false), ENCARG(0))
   ENCARG(cons_app(s, false)) -> c12(APP(s, false), ENCARG(s))
   ENCARG(cons_app(quot, false)) -> c12(APP(quot, false), ENCARG(quot))
   ENCARG(cons_app(plus, false)) -> c12(APP(plus, false), ENCARG(plus))
   ENCARG(cons_app(map, false)) -> c12(APP(map, false), ENCARG(map))
   ENCARG(cons_app(nil, false)) -> c12(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(cons, false)) -> c12(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(filter, false)) -> c12(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(filter2, false)) -> c12(APP(filter2, false), ENCARG(filter2))
   ENCARG(cons_app(true, false)) -> c12(APP(true, false), ENCARG(true))
   ENCARG(cons_app(false, false)) -> c12(APP(false, false), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2


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

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(0, false)) -> c12(APP(0, false), ENCARG(0))
   ENCARG(cons_app(minus, false)) -> c12(APP(minus, false), ENCARG(minus))
   ENCARG(cons_app(true, false)) -> c12(APP(true, false), ENCARG(true))
   ENCARG(cons_app(filter, false)) -> c12(APP(filter, false), ENCARG(filter))
   ENCARG(cons_app(nil, false)) -> c12(APP(nil, false), ENCARG(nil))
   ENCARG(cons_app(plus, false)) -> c12(APP(plus, false), ENCARG(plus))
   ENCARG(cons_app(false, false)) -> c12(APP(false, false), ENCARG(false))
   ENCARG(cons_app(map, false)) -> c12(APP(map, false), ENCARG(map))
   ENCARG(cons_app(cons, false)) -> c12(APP(cons, false), ENCARG(cons))
   ENCARG(cons_app(quot, false)) -> c12(APP(quot, false), ENCARG(quot))
   ENCARG(cons_app(s, false)) -> c12(APP(s, false), ENCARG(s))
   ENCARG(cons_app(filter2, false)) -> c12(APP(filter2, false), ENCARG(filter2))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(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:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(quot, app(s, app(s, z0))), app(s, app(s, z1))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, z1))), APP(app(minus, app(s, z0)), app(s, z1))) by 
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) by 
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(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))) by 
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, 0), app(quot, 0)), app(s, z0)), x2)), app(filter, app(quot, 0))), app(app(cons, app(s, z0)), x2)), x3), APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))), app(quot, app(s, z0))), app(s, z1)), x2)), app(filter, app(quot, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(app(plus, z0), z1))), app(plus, app(s, z0))), z1), x2)), app(filter, app(plus, app(s, z0)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))), app(plus, app(app(minus, z0), app(s, 0)))), app(app(minus, z1), app(s, app(s, z2)))), x2)), app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3), APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))), app(plus, app(app(plus, z0), app(s, 0)))), app(app(plus, z1), app(s, app(s, z2)))), x2)), app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3), APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(map, z0)), nil), x2)), app(filter, app(map, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(map, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(filter, z0)), nil), x2)), app(filter, app(filter, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, 0), app(quot, 0)), app(s, z0)), x2)), app(filter, app(quot, 0))), app(app(cons, app(s, z0)), x2)), x3), APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))), app(quot, app(s, z0))), app(s, z1)), x2)), app(filter, app(quot, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(app(plus, z0), z1))), app(plus, app(s, z0))), z1), x2)), app(filter, app(plus, app(s, z0)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))), app(plus, app(app(minus, z0), app(s, 0)))), app(app(minus, z1), app(s, app(s, z2)))), x2)), app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3), APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))), app(plus, app(app(plus, z0), app(s, 0)))), app(app(plus, z1), app(s, app(s, z2)))), x2)), app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3), APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(map, z0)), nil), x2)), app(filter, app(map, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(map, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(filter, z0)), nil), x2)), app(filter, app(filter, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, 0), app(quot, 0)), app(s, z0)), x2)), app(filter, app(quot, 0))), app(app(cons, app(s, z0)), x2)), x3), APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))), app(quot, app(s, z0))), app(s, z1)), x2)), app(filter, app(quot, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(app(plus, z0), z1))), app(plus, app(s, z0))), z1), x2)), app(filter, app(plus, app(s, z0)))), app(app(cons, z1), x2)), x3), APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))), app(plus, app(app(minus, z0), app(s, 0)))), app(app(minus, z1), app(s, app(s, z2)))), x2)), app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3), APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))), app(plus, app(app(plus, z0), app(s, 0)))), app(app(plus, z1), app(s, app(s, z2)))), x2)), app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3), APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(map, z0)), nil), x2)), app(filter, app(map, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(map, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(filter, z0)), nil), x2)), app(filter, app(filter, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 9 trailing tuple parts
----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c37(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(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c37(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)) by 
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, nil), app(app(app(filter2, false), z0), x1)), nil), x3), APP(app(app(app(filter2, false), z0), x1), nil))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, nil), app(app(app(filter2, false), z0), x1)), nil), x3), APP(app(app(app(filter2, false), z0), x1), nil))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, nil), app(app(app(filter2, false), z0), x1)), nil), x3), APP(app(app(app(filter2, false), z0), x1), nil))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) by 
   ENCODE_APP(minus, minus) -> c(APP(minus, minus))
   ENCODE_APP(0, minus) -> c(APP(0, minus))
   ENCODE_APP(s, minus) -> c(APP(s, minus))
   ENCODE_APP(quot, minus) -> c(APP(quot, minus))
   ENCODE_APP(plus, minus) -> c(APP(plus, minus))
   ENCODE_APP(map, minus) -> c(APP(map, minus))
   ENCODE_APP(nil, minus) -> c(APP(nil, minus))
   ENCODE_APP(cons, minus) -> c(APP(cons, minus))
   ENCODE_APP(filter, minus) -> c(APP(filter, minus))
   ENCODE_APP(filter2, minus) -> c(APP(filter2, minus))
   ENCODE_APP(true, minus) -> c(APP(true, minus))
   ENCODE_APP(false, minus) -> c(APP(false, minus))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(minus, minus) -> c(APP(minus, minus))
   ENCODE_APP(0, minus) -> c(APP(0, minus))
   ENCODE_APP(s, minus) -> c(APP(s, minus))
   ENCODE_APP(quot, minus) -> c(APP(quot, minus))
   ENCODE_APP(plus, minus) -> c(APP(plus, minus))
   ENCODE_APP(map, minus) -> c(APP(map, minus))
   ENCODE_APP(nil, minus) -> c(APP(nil, minus))
   ENCODE_APP(cons, minus) -> c(APP(cons, minus))
   ENCODE_APP(filter, minus) -> c(APP(filter, minus))
   ENCODE_APP(filter2, minus) -> c(APP(filter2, minus))
   ENCODE_APP(true, minus) -> c(APP(true, minus))
   ENCODE_APP(false, minus) -> c(APP(false, minus))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(true, minus) -> c(APP(true, minus))
   ENCODE_APP(cons, minus) -> c(APP(cons, minus))
   ENCODE_APP(quot, minus) -> c(APP(quot, minus))
   ENCODE_APP(map, minus) -> c(APP(map, minus))
   ENCODE_APP(filter2, minus) -> c(APP(filter2, minus))
   ENCODE_APP(0, minus) -> c(APP(0, minus))
   ENCODE_APP(minus, minus) -> c(APP(minus, minus))
   ENCODE_APP(false, minus) -> c(APP(false, minus))
   ENCODE_APP(plus, minus) -> c(APP(plus, minus))
   ENCODE_APP(nil, minus) -> c(APP(nil, minus))
   ENCODE_APP(filter, minus) -> c(APP(filter, minus))
   ENCODE_APP(s, minus) -> c(APP(s, minus))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) by 
   ENCODE_APP(minus, 0) -> c(APP(minus, 0))
   ENCODE_APP(0, 0) -> c(APP(0, 0))
   ENCODE_APP(s, 0) -> c(APP(s, 0))
   ENCODE_APP(quot, 0) -> c(APP(quot, 0))
   ENCODE_APP(plus, 0) -> c(APP(plus, 0))
   ENCODE_APP(map, 0) -> c(APP(map, 0))
   ENCODE_APP(nil, 0) -> c(APP(nil, 0))
   ENCODE_APP(cons, 0) -> c(APP(cons, 0))
   ENCODE_APP(filter, 0) -> c(APP(filter, 0))
   ENCODE_APP(filter2, 0) -> c(APP(filter2, 0))
   ENCODE_APP(true, 0) -> c(APP(true, 0))
   ENCODE_APP(false, 0) -> c(APP(false, 0))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(minus, 0) -> c(APP(minus, 0))
   ENCODE_APP(0, 0) -> c(APP(0, 0))
   ENCODE_APP(s, 0) -> c(APP(s, 0))
   ENCODE_APP(quot, 0) -> c(APP(quot, 0))
   ENCODE_APP(plus, 0) -> c(APP(plus, 0))
   ENCODE_APP(map, 0) -> c(APP(map, 0))
   ENCODE_APP(nil, 0) -> c(APP(nil, 0))
   ENCODE_APP(cons, 0) -> c(APP(cons, 0))
   ENCODE_APP(filter, 0) -> c(APP(filter, 0))
   ENCODE_APP(filter2, 0) -> c(APP(filter2, 0))
   ENCODE_APP(true, 0) -> c(APP(true, 0))
   ENCODE_APP(false, 0) -> c(APP(false, 0))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(nil, 0) -> c(APP(nil, 0))
   ENCODE_APP(map, 0) -> c(APP(map, 0))
   ENCODE_APP(false, 0) -> c(APP(false, 0))
   ENCODE_APP(filter, 0) -> c(APP(filter, 0))
   ENCODE_APP(s, 0) -> c(APP(s, 0))
   ENCODE_APP(true, 0) -> c(APP(true, 0))
   ENCODE_APP(filter2, 0) -> c(APP(filter2, 0))
   ENCODE_APP(0, 0) -> c(APP(0, 0))
   ENCODE_APP(cons, 0) -> c(APP(cons, 0))
   ENCODE_APP(plus, 0) -> c(APP(plus, 0))
   ENCODE_APP(quot, 0) -> c(APP(quot, 0))
   ENCODE_APP(minus, 0) -> c(APP(minus, 0))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, s) -> c(APP(encArg(x0), s))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) by 
   ENCODE_APP(minus, s) -> c(APP(minus, s))
   ENCODE_APP(0, s) -> c(APP(0, s))
   ENCODE_APP(s, s) -> c(APP(s, s))
   ENCODE_APP(quot, s) -> c(APP(quot, s))
   ENCODE_APP(plus, s) -> c(APP(plus, s))
   ENCODE_APP(map, s) -> c(APP(map, s))
   ENCODE_APP(nil, s) -> c(APP(nil, s))
   ENCODE_APP(cons, s) -> c(APP(cons, s))
   ENCODE_APP(filter, s) -> c(APP(filter, s))
   ENCODE_APP(filter2, s) -> c(APP(filter2, s))
   ENCODE_APP(true, s) -> c(APP(true, s))
   ENCODE_APP(false, s) -> c(APP(false, s))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(minus, s) -> c(APP(minus, s))
   ENCODE_APP(0, s) -> c(APP(0, s))
   ENCODE_APP(s, s) -> c(APP(s, s))
   ENCODE_APP(quot, s) -> c(APP(quot, s))
   ENCODE_APP(plus, s) -> c(APP(plus, s))
   ENCODE_APP(map, s) -> c(APP(map, s))
   ENCODE_APP(nil, s) -> c(APP(nil, s))
   ENCODE_APP(cons, s) -> c(APP(cons, s))
   ENCODE_APP(filter, s) -> c(APP(filter, s))
   ENCODE_APP(filter2, s) -> c(APP(filter2, s))
   ENCODE_APP(true, s) -> c(APP(true, s))
   ENCODE_APP(false, s) -> c(APP(false, s))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(filter, s) -> c(APP(filter, s))
   ENCODE_APP(false, s) -> c(APP(false, s))
   ENCODE_APP(s, s) -> c(APP(s, s))
   ENCODE_APP(true, s) -> c(APP(true, s))
   ENCODE_APP(filter2, s) -> c(APP(filter2, s))
   ENCODE_APP(cons, s) -> c(APP(cons, s))
   ENCODE_APP(quot, s) -> c(APP(quot, s))
   ENCODE_APP(minus, s) -> c(APP(minus, s))
   ENCODE_APP(plus, s) -> c(APP(plus, s))
   ENCODE_APP(0, s) -> c(APP(0, s))
   ENCODE_APP(nil, s) -> c(APP(nil, s))
   ENCODE_APP(map, s) -> c(APP(map, s))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot)) by 
   ENCODE_APP(minus, quot) -> c(APP(minus, quot))
   ENCODE_APP(0, quot) -> c(APP(0, quot))
   ENCODE_APP(s, quot) -> c(APP(s, quot))
   ENCODE_APP(quot, quot) -> c(APP(quot, quot))
   ENCODE_APP(plus, quot) -> c(APP(plus, quot))
   ENCODE_APP(map, quot) -> c(APP(map, quot))
   ENCODE_APP(nil, quot) -> c(APP(nil, quot))
   ENCODE_APP(cons, quot) -> c(APP(cons, quot))
   ENCODE_APP(filter, quot) -> c(APP(filter, quot))
   ENCODE_APP(filter2, quot) -> c(APP(filter2, quot))
   ENCODE_APP(true, quot) -> c(APP(true, quot))
   ENCODE_APP(false, quot) -> c(APP(false, quot))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(minus, quot) -> c(APP(minus, quot))
   ENCODE_APP(0, quot) -> c(APP(0, quot))
   ENCODE_APP(s, quot) -> c(APP(s, quot))
   ENCODE_APP(quot, quot) -> c(APP(quot, quot))
   ENCODE_APP(plus, quot) -> c(APP(plus, quot))
   ENCODE_APP(map, quot) -> c(APP(map, quot))
   ENCODE_APP(nil, quot) -> c(APP(nil, quot))
   ENCODE_APP(cons, quot) -> c(APP(cons, quot))
   ENCODE_APP(filter, quot) -> c(APP(filter, quot))
   ENCODE_APP(filter2, quot) -> c(APP(filter2, quot))
   ENCODE_APP(true, quot) -> c(APP(true, quot))
   ENCODE_APP(false, quot) -> c(APP(false, quot))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(false, quot) -> c(APP(false, quot))
   ENCODE_APP(filter, quot) -> c(APP(filter, quot))
   ENCODE_APP(cons, quot) -> c(APP(cons, quot))
   ENCODE_APP(quot, quot) -> c(APP(quot, quot))
   ENCODE_APP(plus, quot) -> c(APP(plus, quot))
   ENCODE_APP(filter2, quot) -> c(APP(filter2, quot))
   ENCODE_APP(0, quot) -> c(APP(0, quot))
   ENCODE_APP(true, quot) -> c(APP(true, quot))
   ENCODE_APP(minus, quot) -> c(APP(minus, quot))
   ENCODE_APP(nil, quot) -> c(APP(nil, quot))
   ENCODE_APP(map, quot) -> c(APP(map, quot))
   ENCODE_APP(s, quot) -> c(APP(s, quot))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, plus) -> c(APP(encArg(x0), plus)) by 
   ENCODE_APP(minus, plus) -> c(APP(minus, plus))
   ENCODE_APP(0, plus) -> c(APP(0, plus))
   ENCODE_APP(s, plus) -> c(APP(s, plus))
   ENCODE_APP(quot, plus) -> c(APP(quot, plus))
   ENCODE_APP(plus, plus) -> c(APP(plus, plus))
   ENCODE_APP(map, plus) -> c(APP(map, plus))
   ENCODE_APP(nil, plus) -> c(APP(nil, plus))
   ENCODE_APP(cons, plus) -> c(APP(cons, plus))
   ENCODE_APP(filter, plus) -> c(APP(filter, plus))
   ENCODE_APP(filter2, plus) -> c(APP(filter2, plus))
   ENCODE_APP(true, plus) -> c(APP(true, plus))
   ENCODE_APP(false, plus) -> c(APP(false, plus))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(minus, plus) -> c(APP(minus, plus))
   ENCODE_APP(0, plus) -> c(APP(0, plus))
   ENCODE_APP(s, plus) -> c(APP(s, plus))
   ENCODE_APP(quot, plus) -> c(APP(quot, plus))
   ENCODE_APP(plus, plus) -> c(APP(plus, plus))
   ENCODE_APP(map, plus) -> c(APP(map, plus))
   ENCODE_APP(nil, plus) -> c(APP(nil, plus))
   ENCODE_APP(cons, plus) -> c(APP(cons, plus))
   ENCODE_APP(filter, plus) -> c(APP(filter, plus))
   ENCODE_APP(filter2, plus) -> c(APP(filter2, plus))
   ENCODE_APP(true, plus) -> c(APP(true, plus))
   ENCODE_APP(false, plus) -> c(APP(false, plus))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(plus, plus) -> c(APP(plus, plus))
   ENCODE_APP(true, plus) -> c(APP(true, plus))
   ENCODE_APP(nil, plus) -> c(APP(nil, plus))
   ENCODE_APP(s, plus) -> c(APP(s, plus))
   ENCODE_APP(filter2, plus) -> c(APP(filter2, plus))
   ENCODE_APP(filter, plus) -> c(APP(filter, plus))
   ENCODE_APP(cons, plus) -> c(APP(cons, plus))
   ENCODE_APP(quot, plus) -> c(APP(quot, plus))
   ENCODE_APP(false, plus) -> c(APP(false, plus))
   ENCODE_APP(minus, plus) -> c(APP(minus, plus))
   ENCODE_APP(map, plus) -> c(APP(map, plus))
   ENCODE_APP(0, plus) -> c(APP(0, plus))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) by 
   ENCODE_APP(minus, map) -> c(APP(minus, map))
   ENCODE_APP(0, map) -> c(APP(0, map))
   ENCODE_APP(s, map) -> c(APP(s, map))
   ENCODE_APP(quot, map) -> c(APP(quot, map))
   ENCODE_APP(plus, map) -> c(APP(plus, map))
   ENCODE_APP(map, map) -> c(APP(map, map))
   ENCODE_APP(nil, map) -> c(APP(nil, map))
   ENCODE_APP(cons, map) -> c(APP(cons, map))
   ENCODE_APP(filter, map) -> c(APP(filter, map))
   ENCODE_APP(filter2, map) -> c(APP(filter2, map))
   ENCODE_APP(true, map) -> c(APP(true, map))
   ENCODE_APP(false, map) -> c(APP(false, map))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
   ENCODE_APP(minus, map) -> c(APP(minus, map))
   ENCODE_APP(0, map) -> c(APP(0, map))
   ENCODE_APP(s, map) -> c(APP(s, map))
   ENCODE_APP(quot, map) -> c(APP(quot, map))
   ENCODE_APP(plus, map) -> c(APP(plus, map))
   ENCODE_APP(map, map) -> c(APP(map, map))
   ENCODE_APP(nil, map) -> c(APP(nil, map))
   ENCODE_APP(cons, map) -> c(APP(cons, map))
   ENCODE_APP(filter, map) -> c(APP(filter, map))
   ENCODE_APP(filter2, map) -> c(APP(filter2, map))
   ENCODE_APP(true, map) -> c(APP(true, map))
   ENCODE_APP(false, map) -> c(APP(false, map))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(true, map) -> c(APP(true, map))
   ENCODE_APP(plus, map) -> c(APP(plus, map))
   ENCODE_APP(map, map) -> c(APP(map, map))
   ENCODE_APP(s, map) -> c(APP(s, map))
   ENCODE_APP(0, map) -> c(APP(0, map))
   ENCODE_APP(cons, map) -> c(APP(cons, map))
   ENCODE_APP(quot, map) -> c(APP(quot, map))
   ENCODE_APP(filter2, map) -> c(APP(filter2, map))
   ENCODE_APP(false, map) -> c(APP(false, map))
   ENCODE_APP(minus, map) -> c(APP(minus, map))
   ENCODE_APP(nil, map) -> c(APP(nil, map))
   ENCODE_APP(filter, map) -> c(APP(filter, map))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) by 
   ENCODE_APP(minus, nil) -> c(APP(minus, nil))
   ENCODE_APP(0, nil) -> c(APP(0, nil))
   ENCODE_APP(s, nil) -> c(APP(s, nil))
   ENCODE_APP(quot, nil) -> c(APP(quot, nil))
   ENCODE_APP(plus, nil) -> c(APP(plus, nil))
   ENCODE_APP(map, nil) -> c(APP(map, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(filter, nil) -> c(APP(filter, nil))
   ENCODE_APP(filter2, nil) -> c(APP(filter2, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(minus, nil) -> c(APP(minus, nil))
   ENCODE_APP(0, nil) -> c(APP(0, nil))
   ENCODE_APP(s, nil) -> c(APP(s, nil))
   ENCODE_APP(quot, nil) -> c(APP(quot, nil))
   ENCODE_APP(plus, nil) -> c(APP(plus, nil))
   ENCODE_APP(map, nil) -> c(APP(map, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(filter, nil) -> c(APP(filter, nil))
   ENCODE_APP(filter2, nil) -> c(APP(filter2, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(false, nil) -> c(APP(false, nil))
   ENCODE_APP(filter2, nil) -> c(APP(filter2, nil))
   ENCODE_APP(0, nil) -> c(APP(0, nil))
   ENCODE_APP(true, nil) -> c(APP(true, nil))
   ENCODE_APP(plus, nil) -> c(APP(plus, nil))
   ENCODE_APP(nil, nil) -> c(APP(nil, nil))
   ENCODE_APP(s, nil) -> c(APP(s, nil))
   ENCODE_APP(cons, nil) -> c(APP(cons, nil))
   ENCODE_APP(quot, nil) -> c(APP(quot, nil))
   ENCODE_APP(filter, nil) -> c(APP(filter, nil))
   ENCODE_APP(map, nil) -> c(APP(map, nil))
   ENCODE_APP(minus, nil) -> c(APP(minus, nil))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   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, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(155) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) by 
   ENCODE_APP(minus, cons) -> c(APP(minus, cons))
   ENCODE_APP(0, cons) -> c(APP(0, cons))
   ENCODE_APP(s, cons) -> c(APP(s, cons))
   ENCODE_APP(quot, cons) -> c(APP(quot, cons))
   ENCODE_APP(plus, cons) -> c(APP(plus, cons))
   ENCODE_APP(map, cons) -> c(APP(map, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(filter, cons) -> c(APP(filter, cons))
   ENCODE_APP(filter2, cons) -> c(APP(filter2, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(minus, cons) -> c(APP(minus, cons))
   ENCODE_APP(0, cons) -> c(APP(0, cons))
   ENCODE_APP(s, cons) -> c(APP(s, cons))
   ENCODE_APP(quot, cons) -> c(APP(quot, cons))
   ENCODE_APP(plus, cons) -> c(APP(plus, cons))
   ENCODE_APP(map, cons) -> c(APP(map, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(filter, cons) -> c(APP(filter, cons))
   ENCODE_APP(filter2, cons) -> c(APP(filter2, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(s, cons) -> c(APP(s, cons))
   ENCODE_APP(map, cons) -> c(APP(map, cons))
   ENCODE_APP(filter, cons) -> c(APP(filter, cons))
   ENCODE_APP(plus, cons) -> c(APP(plus, cons))
   ENCODE_APP(false, cons) -> c(APP(false, cons))
   ENCODE_APP(filter2, cons) -> c(APP(filter2, cons))
   ENCODE_APP(minus, cons) -> c(APP(minus, cons))
   ENCODE_APP(0, cons) -> c(APP(0, cons))
   ENCODE_APP(true, cons) -> c(APP(true, cons))
   ENCODE_APP(cons, cons) -> c(APP(cons, cons))
   ENCODE_APP(quot, cons) -> c(APP(quot, cons))
   ENCODE_APP(nil, cons) -> c(APP(nil, cons))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(159) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) by 
   ENCODE_APP(minus, filter) -> c(APP(minus, filter))
   ENCODE_APP(0, filter) -> c(APP(0, filter))
   ENCODE_APP(s, filter) -> c(APP(s, filter))
   ENCODE_APP(quot, filter) -> c(APP(quot, filter))
   ENCODE_APP(plus, filter) -> c(APP(plus, filter))
   ENCODE_APP(map, filter) -> c(APP(map, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(filter2, filter) -> c(APP(filter2, filter))
   ENCODE_APP(true, filter) -> c(APP(true, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(minus, filter) -> c(APP(minus, filter))
   ENCODE_APP(0, filter) -> c(APP(0, filter))
   ENCODE_APP(s, filter) -> c(APP(s, filter))
   ENCODE_APP(quot, filter) -> c(APP(quot, filter))
   ENCODE_APP(plus, filter) -> c(APP(plus, filter))
   ENCODE_APP(map, filter) -> c(APP(map, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(filter2, filter) -> c(APP(filter2, filter))
   ENCODE_APP(true, filter) -> c(APP(true, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1


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

(161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(true, filter) -> c(APP(true, filter))
   ENCODE_APP(minus, filter) -> c(APP(minus, filter))
   ENCODE_APP(nil, filter) -> c(APP(nil, filter))
   ENCODE_APP(filter, filter) -> c(APP(filter, filter))
   ENCODE_APP(s, filter) -> c(APP(s, filter))
   ENCODE_APP(map, filter) -> c(APP(map, filter))
   ENCODE_APP(cons, filter) -> c(APP(cons, filter))
   ENCODE_APP(quot, filter) -> c(APP(quot, filter))
   ENCODE_APP(false, filter) -> c(APP(false, filter))
   ENCODE_APP(filter2, filter) -> c(APP(filter2, filter))
   ENCODE_APP(plus, filter) -> c(APP(plus, filter))
   ENCODE_APP(0, filter) -> c(APP(0, filter))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(plus) -> plus
   encArg(map) -> map
   encArg(nil) -> nil
   encArg(cons) -> cons
   encArg(filter) -> filter
   encArg(filter2) -> filter2
   encArg(true) -> true
   encArg(false) -> false
   encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1))
   app(app(minus, z0), 0) -> z0
   app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1)
   app(app(quot, 0), app(s, z0)) -> 0
   app(app(quot, app(s, z0)), app(s, z1)) -> app(s, app(app(quot, app(app(minus, z0), z1)), app(s, z1)))
   app(app(plus, 0), z0) -> z0
   app(app(plus, app(s, z0)), z1) -> app(s, app(app(plus, z0), z1))
   app(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(minus, z1), app(s, app(s, z2)))), app(app(minus, z0), app(s, 0)))
   app(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> app(app(plus, app(app(plus, z1), app(s, app(s, z2)))), app(app(plus, z0), app(s, 0)))
   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(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   ENCARG(cons_app(minus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(quot, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(plus, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(map, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(filter2, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1))
   ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2))
   ENCODE_APP(x0, true) -> c(APP(encArg(x0), true))
   ENCODE_APP(x0, false) -> c(APP(encArg(x0), false))
   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, minus))) -> c12(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus)))
   ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0)))
   ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s)))
   ENCARG(cons_app(x0, cons_app(x1, quot))) -> c12(APP(encArg(x0), app(encArg(x1), quot)), ENCARG(x0), ENCARG(cons_app(x1, quot)))
   ENCARG(cons_app(x0, cons_app(x1, plus))) -> c12(APP(encArg(x0), app(encArg(x1), plus)), ENCARG(x0), ENCARG(cons_app(x1, plus)))
   ENCARG(cons_app(x0, cons_app(x1, map))) -> c12(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map)))
   ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil)))
   ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons)))
   ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter)))
   ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c12(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2)))
   ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true)))
   ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false)))
   ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(minus, x2))) -> c12(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2)))
   ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2)))
   ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2)))
   ENCARG(cons_app(x0, cons_app(quot, x2))) -> c12(APP(encArg(x0), app(quot, encArg(x2))), ENCARG(x0), ENCARG(cons_app(quot, x2)))
   ENCARG(cons_app(x0, cons_app(plus, x2))) -> c12(APP(encArg(x0), app(plus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(plus, x2)))
   ENCARG(cons_app(x0, cons_app(map, x2))) -> c12(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2)))
   ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2)))
   ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2)))
   ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2)))
   ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c12(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2)))
   ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2)))
   ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2)))
   ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(minus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(quot, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(plus, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(map, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2)))
   ENCARG(cons_app(cons_app(x0, minus), x2)) -> c12(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, quot), x2)) -> c12(APP(app(encArg(x0), quot), encArg(x2)), ENCARG(cons_app(x0, quot)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, plus), x2)) -> c12(APP(app(encArg(x0), plus), encArg(x2)), ENCARG(cons_app(x0, plus)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, map), x2)) -> c12(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c12(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2))
   ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(minus, x1), x2)) -> c12(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(quot, x1), x2)) -> c12(APP(app(quot, encArg(x1)), encArg(x2)), ENCARG(cons_app(quot, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(plus, x1), x2)) -> c12(APP(app(plus, encArg(x1)), encArg(x2)), ENCARG(cons_app(plus, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(map, x1), x2)) -> c12(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), minus)) -> c12(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), quot)) -> c12(APP(app(encArg(x0), encArg(x1)), quot), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), plus)) -> c12(APP(app(encArg(x0), encArg(x1)), plus), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), map)) -> c12(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c12(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)))
   ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c12(ENCARG(cons_app(filter2, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2))
   ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
   ENCODE_APP(cons_app(z0, z1), minus) -> c(APP(app(encArg(z0), encArg(z1)), minus))
   ENCODE_APP(cons_app(z0, z1), 0) -> c(APP(app(encArg(z0), encArg(z1)), 0))
   ENCODE_APP(cons_app(z0, z1), s) -> c(APP(app(encArg(z0), encArg(z1)), s))
   ENCODE_APP(cons_app(z0, z1), quot) -> c(APP(app(encArg(z0), encArg(z1)), quot))
   ENCODE_APP(cons_app(z0, z1), plus) -> c(APP(app(encArg(z0), encArg(z1)), plus))
   ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map))
   ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil))
   ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons))
   ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(app(plus, 0), z0) -> c30
   APP(app(map, z0), nil) -> c34
   APP(app(filter, z0), nil) -> c36
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(plus, app(s, z0)), z1) -> c31(APP(app(plus, z0), z1))
   APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))) -> c33(APP(app(plus, z1), app(s, app(s, z2))), APP(app(plus, z0), app(s, 0)))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c35(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c38(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c39(APP(app(filter, z0), z2))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z1), app(s, app(s, z2))))
   APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))) -> c(APP(app(minus, z0), app(s, 0)))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)) -> c37(APP(app(app(app(filter2, z0), app(plus, 0)), z0), x2), APP(app(plus, 0), z0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c37(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c37(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)) -> c37(APP(app(plus, app(s, z0)), z1))
   APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(minus, z0), app(s, 0))), app(app(minus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)) -> c37(APP(app(plus, app(app(plus, z0), app(s, 0))), app(app(plus, z1), app(s, app(s, z2)))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c37(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c37(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c37(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c37(APP(app(app(app(filter2, true), z0), z1), z2))
   APP(app(quot, app(s, app(s, z0))), app(s, app(s, 0))) -> c29(APP(app(quot, z0), app(s, app(s, 0))), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(quot, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c29(APP(app(quot, app(app(minus, z0), z1)), app(s, app(s, app(s, z1)))), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(quot, app(s, app(s, x0))), app(s, app(s, x1))) -> c29(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c37(APP(app(app(app(filter2, z0), app(minus, app(s, z0))), app(s, 0)), x2), APP(app(minus, app(s, z0)), app(s, 0)))
   APP(app(filter, app(minus, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c37(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, app(s, z0)))), app(s, app(s, z1))), x2), APP(app(minus, app(s, app(s, z0))), app(s, app(s, z1))))
   APP(app(filter, app(minus, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c37(APP(app(minus, app(s, x0)), app(s, x1)))
   APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(minus, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(minus, z0)), 0), x2)), app(filter, app(minus, z0))), app(app(cons, 0), x2)), x3), APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)))
   APP(app(filter, app(filter, app(minus, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2)), app(filter, app(minus, app(s, z0)))), app(app(cons, app(s, z1)), x2)), x3), APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(plus, 0)), z0), x2)), app(filter, app(plus, 0))), app(app(cons, z0), x2)), x3), APP(app(filter, app(plus, 0)), app(app(cons, z0), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(app(app(filter2, 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(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c37(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)))
   APP(app(filter, app(filter, app(quot, 0))), app(app(cons, app(app(cons, app(s, z0)), x2)), x3)) -> c37(APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)))
   APP(app(filter, app(filter, app(quot, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c37(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, app(plus, app(s, z0)))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c37(APP(app(filter, app(plus, app(s, z0))), app(app(cons, z1), x2)))
   APP(app(filter, app(filter, app(plus, app(app(minus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(minus, z0), app(s, 0)))), app(app(cons, app(app(minus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(plus, app(app(plus, z0), app(s, 0))))), app(app(cons, app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)), x3)) -> c37(APP(app(filter, app(plus, app(app(plus, z0), app(s, 0)))), app(app(cons, app(app(plus, z1), app(s, app(s, z2)))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c37(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)))
   APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c37(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c37(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2)))
   APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c37(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c37(APP(app(app(app(filter2, false), z0), x1), nil))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCARG_1, ENCODE_APP_2

Compound Symbols:   c26, c28, c30, c34, c36, c27_1, c31_1, c33_2, c35_2, c38_1, c39_1, c_1, c12_1, c29_2, c37_2, c37_1, c12_3, c12_2, c29_1