/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 192 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 3 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 60.4 s]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 38 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 15 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(36) CdtProblem
    (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 17 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms]
    (66) CdtProblem
    (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 103 ms]
    (70) CdtProblem
    (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 54 ms]
    (72) CdtProblem
    (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms]
    (76) CdtProblem
    (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 6 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms]
    (84) CdtProblem
    (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
    (90) CdtProblem
    (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms]
    (102) CdtProblem
    (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms]
    (106) CdtProblem
    (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
    (118) CdtProblem
    (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 5 ms]
    (124) CdtProblem
    (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
    (128) CdtProblem
    (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms]
    (154) CdtProblem
    (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (160) CdtProblem
    (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (168) 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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, 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(log) -> log
   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_log -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, 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(log) -> log
   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_log -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, 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(log) -> log
   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_log -> log
   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) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

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

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


The TRS R consists of the following rules:

   app(app(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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, 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(log) -> log
   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_log -> log
   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) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

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


The TRS R consists of the following rules:

   app(app(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(log, app(s, 0')) -> 0'
   app(log, app(s, app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, 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(log) -> log
   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_log -> log
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

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

(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(log, app(s, 0')) -> 0'
app(log, app(s, app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, 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(log) -> log
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_log -> log
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:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
minus :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
0' :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
s :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
quot :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
log :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
map :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
nil :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
cons :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
filter :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
filter2 :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
true :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
false :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encArg :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
cons_app :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_app :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_minus :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_0 :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_s :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_quot :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_log :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_map :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_nil :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_cons :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter2 :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_true :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_false :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
hole_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app1_3 :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
gen_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app2_3 :: Nat -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app

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

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

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

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

(12)
Obligation:
Innermost TRS:
Rules:
app(app(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(log, app(s, 0')) -> 0'
app(log, app(s, app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, 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(log) -> log
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_log -> log
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:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
minus :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
0' :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
s :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
quot :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
log :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
map :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
nil :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
cons :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
filter :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
filter2 :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
true :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
false :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encArg :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
cons_app :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_app :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_minus :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_0 :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_s :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_quot :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_log :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_map :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_nil :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_cons :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_filter2 :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_true :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
encode_false :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
hole_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app1_3 :: minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app
gen_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app2_3 :: Nat -> minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app


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

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

(13) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app2_3(n58773_3)) -> *3_3, rt in Omega(0)

Induction Base:
encArg(gen_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app2_3(0))

Induction Step:
encArg(gen_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app2_3(+(n58773_3, 1))) ->_R^Omega(0)
app(encArg(minus), encArg(gen_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app2_3(n58773_3))) ->_R^Omega(0)
app(minus, encArg(gen_minus:0':s:quot:log:map:nil:cons:filter:filter2:true:false:cons_app2_3(n58773_3))) ->_IH
app(minus, *3_3)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(14)
BOUNDS(1, INF)

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

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

(16)
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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, 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(log) -> log
   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_log -> log
   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
----------------------------------------

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

(18)
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(log, c_app(s, 0)) -> 0
   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(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(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(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
   app(c_app(minus, x), 0) -> x
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, app(s, 0))))))
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y)
   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)))

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

   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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_log -> log
   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
----------------------------------------

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

(20)
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(log, c_app(s, 0)) -> 0 [1]
   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(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(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(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, x), 0) -> x [1]
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, app(s, 0)))))) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [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]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(log) -> log [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_log -> log [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
----------------------------------------

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

(22)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   app(log, c_app(s, 0)) -> 0 [1]
   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(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(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(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, x), 0) -> x [1]
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, app(s, 0)))))) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [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]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(log) -> log [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_log -> log [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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
c_app :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
s :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
0 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
map :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
cons :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
quot :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
filter2 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
true :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
filter :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
false :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
nil :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
minus :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encArg :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
cons_app :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_app :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_minus :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_0 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_s :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_quot :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_map :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_nil :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_cons :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_filter :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_filter2 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_true :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app
encode_false :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app

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

(23) 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_log
   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_log -> null_encode_log [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_log, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app

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

(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(log, c_app(s, 0)) -> 0 [1]
   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(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(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(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, x), 0) -> x [1]
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, app(s, 0)))))) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [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]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(log) -> log [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_log -> log [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_log -> null_encode_log [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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
s :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
0 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
quot :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
minus :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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_log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(26)
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(log, c_app(s, 0)) -> 0 [1]
   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(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(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(filter, log), c_app(c_app(cons, c_app(s, 0)), xs)) -> app(app(app(app(filter2, 0), log), c_app(s, 0)), xs) [2]
   app(c_app(filter, c_app(map, f5)), c_app(c_app(cons, c_app(c_app(cons, x8), xs1)), xs)) -> app(app(app(app(filter2, app(app(cons, app(f5, x8)), app(app(map, f5), xs1))), c_app(map, f5)), c_app(c_app(cons, x8), xs1)), xs) [2]
   app(c_app(filter, c_app(quot, 0)), c_app(c_app(cons, c_app(s, y2)), xs)) -> app(app(app(app(filter2, 0), c_app(quot, 0)), c_app(s, y2)), xs) [2]
   app(c_app(filter, c_app(c_app(c_app(filter2, true), f6), x9)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(cons, x9), app(app(filter, f6), x))), c_app(c_app(c_app(filter2, true), f6), x9)), x), xs) [2]
   app(c_app(filter, c_app(c_app(c_app(filter2, false), f7), x10)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(filter, f7), x)), c_app(c_app(c_app(filter2, false), f7), x10)), x), xs) [2]
   app(c_app(filter, c_app(map, f8)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(map, f8)), nil), xs) [2]
   app(c_app(filter, c_app(filter, f9)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(filter, f9)), nil), xs) [2]
   app(c_app(filter, c_app(filter, f10)), c_app(c_app(cons, c_app(c_app(cons, x11), xs2)), xs)) -> app(app(app(app(filter2, app(app(app(app(filter2, app(f10, x11)), f10), x11), xs2)), c_app(filter, f10)), c_app(c_app(cons, x11), xs2)), 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, log), c_app(c_app(cons, c_app(s, c_app(s, x13))), xs)) -> app(app(app(app(filter2, app(s, app(log, app(s, app(app(quot, x13), app(s, app(s, 0))))))), log), c_app(s, c_app(s, x13))), xs) [2]
   app(c_app(filter, c_app(minus, c_app(s, x14))), c_app(c_app(cons, c_app(s, y3)), xs)) -> app(app(app(app(filter2, app(app(minus, x14), y3)), c_app(minus, c_app(s, x14))), c_app(s, y3)), xs) [2]
   app(c_app(filter, c_app(quot, c_app(s, x15))), c_app(c_app(cons, c_app(s, y4)), xs)) -> app(app(app(app(filter2, app(s, app(app(quot, app(app(minus, x15), y4)), app(s, y4)))), c_app(quot, c_app(s, x15))), c_app(s, y4)), 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, x), 0) -> x [1]
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(c_app(quot, x), app(s, c_app(s, 0)))))) [1]
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(c_app(quot, x), app(s, null_app))))) [1]
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(null_app, app(s, c_app(s, 0)))))) [1]
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(null_app, app(s, null_app))))) [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(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]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(log) -> log [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_log -> log [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_log -> null_encode_log [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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
s :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
0 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
quot :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
minus :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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_log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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
----------------------------------------

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

   log => 5
   s => 10
   0 => 0
   map => 6
   cons => 1
   quot => 9
   filter2 => 4
   true => 11
   filter => 3
   false => 2
   nil => 8
   minus => 7
   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_log => 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

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

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

   app(z, z') -{ 1 }-> x :|: x >= 0, z = 1 + 7 + x, z' = 0
   app(z, z') -{ 2 }-> app(app(app(app(4, x12), 1 + 7 + x12), 0), xs) :|: xs >= 0, z = 1 + 3 + (1 + 7 + x12), x12 >= 0, z' = 1 + (1 + 1 + 0) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(app(app(4, app(f10, x11)), f10), x11), xs2)), 1 + 3 + f10), 1 + (1 + 1 + x11) + xs2), xs) :|: z = 1 + 3 + (1 + 3 + f10), xs >= 0, xs2 >= 0, z' = 1 + (1 + 1 + (1 + (1 + 1 + x11) + xs2)) + xs, f10 >= 0, x11 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(7, x14), y3)), 1 + 7 + (1 + 10 + x14)), 1 + 10 + y3), xs) :|: xs >= 0, z' = 1 + (1 + 1 + (1 + 10 + y3)) + xs, z = 1 + 3 + (1 + 7 + (1 + 10 + x14)), y3 >= 0, x14 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(3, f7), x)), 1 + (1 + (1 + 4 + 2) + f7) + x10), x), xs) :|: xs >= 0, x >= 0, f7 >= 0, x10 >= 0, z = 1 + 3 + (1 + (1 + (1 + 4 + 2) + f7) + x10), z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(1, x9), app(app(3, f6), x))), 1 + (1 + (1 + 4 + 11) + f6) + x9), x), xs) :|: xs >= 0, z = 1 + 3 + (1 + (1 + (1 + 4 + 11) + f6) + x9), x >= 0, f6 >= 0, x9 >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(1, app(f5, x8)), app(app(6, f5), xs1))), 1 + 6 + f5), 1 + (1 + 1 + x8) + xs1), xs) :|: xs >= 0, x8 >= 0, z = 1 + 3 + (1 + 6 + f5), xs1 >= 0, f5 >= 0, z' = 1 + (1 + 1 + (1 + (1 + 1 + x8) + xs1)) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(10, app(app(9, app(app(7, x15), y4)), app(10, y4)))), 1 + 9 + (1 + 10 + x15)), 1 + 10 + y4), xs) :|: z = 1 + 3 + (1 + 9 + (1 + 10 + x15)), xs >= 0, y4 >= 0, z' = 1 + (1 + 1 + (1 + 10 + y4)) + xs, x15 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(10, app(5, app(10, app(app(9, x13), app(10, app(10, 0))))))), 5), 1 + 10 + (1 + 10 + x13)), xs) :|: z' = 1 + (1 + 1 + (1 + 10 + (1 + 10 + x13))) + xs, x13 >= 0, xs >= 0, z = 1 + 3 + 5
   app(z, z') -{ 2 }-> app(app(app(app(4, 8), 1 + 6 + f8), 8), xs) :|: f8 >= 0, xs >= 0, z' = 1 + (1 + 1 + 8) + xs, z = 1 + 3 + (1 + 6 + f8)
   app(z, z') -{ 2 }-> app(app(app(app(4, 8), 1 + 3 + f9), 8), xs) :|: z = 1 + 3 + (1 + 3 + f9), xs >= 0, z' = 1 + (1 + 1 + 8) + xs, f9 >= 0
   app(z, z') -{ 1 }-> app(app(app(app(4, 0), f), x), xs) :|: z = 1 + 3 + f, f >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, 0), 5), 1 + 10 + 0), xs) :|: xs >= 0, z = 1 + 3 + 5, z' = 1 + (1 + 1 + (1 + 10 + 0)) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, 0), 1 + 9 + 0), 1 + 10 + y2), xs) :|: xs >= 0, z' = 1 + (1 + 1 + (1 + 10 + y2)) + xs, y2 >= 0, z = 1 + 3 + (1 + 9 + 0)
   app(z, z') -{ 1 }-> app(app(app(app(4, 1 + f + x), f), x), xs) :|: z = 1 + 3 + f, f >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(1, app(f, x)), app(app(6, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 6 + f, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(10, app(app(9, app(0, y)), 0)) :|: z = 1 + 9 + (1 + 10 + x), x >= 0, y >= 0, z' = 1 + 10 + y
   app(z, z') -{ 1 }-> app(10, app(app(9, app(0, y)), 1 + 10 + y)) :|: z = 1 + 9 + (1 + 10 + x), x >= 0, y >= 0, z' = 1 + 10 + y
   app(z, z') -{ 1 }-> app(10, app(app(9, app(1 + 7 + x, y)), 0)) :|: z = 1 + 9 + (1 + 10 + x), x >= 0, y >= 0, z' = 1 + 10 + y
   app(z, z') -{ 1 }-> app(10, app(app(9, app(1 + 7 + x, y)), 1 + 10 + y)) :|: z = 1 + 9 + (1 + 10 + x), x >= 0, y >= 0, z' = 1 + 10 + y
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(0, app(10, 0))))) :|: x >= 0, z' = 1 + 10 + (1 + 10 + x), z = 5
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(0, app(10, 1 + 10 + 0))))) :|: x >= 0, z' = 1 + 10 + (1 + 10 + x), z = 5
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(1 + 9 + x, app(10, 0))))) :|: x >= 0, z' = 1 + 10 + (1 + 10 + x), z = 5
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(1 + 9 + x, app(10, 1 + 10 + 0))))) :|: x >= 0, z' = 1 + 10 + (1 + 10 + x), z = 5
   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) :|: x >= 0, y >= 0, z = 1 + 7 + (1 + 10 + x), 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 + 7 + x, y) :|: x >= 0, y >= 0, z = 1 + 7 + (1 + 10 + x), 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 }-> 8 :|: f >= 0, z = 1 + 6 + f, z' = 8
   app(z, z') -{ 1 }-> 8 :|: z = 1 + 3 + f, f >= 0, z' = 8
   app(z, z') -{ 1 }-> 0 :|: z' = 1 + 10 + 0, z = 5
   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 = v0, z' = v1
   app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 9 :|: z = 9
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 11 :|: z = 11
   encArg(z) -{ 0 }-> 10 :|: z = 10
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_0 -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 4 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_log -{ 0 }-> 5 :|: 
   encode_log -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 6 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 7 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 8 :|: 
   encode_nil -{ 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) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

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

   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(app(app(4, app(z - 8, x11)), z - 8), x11), xs2)), 1 + 3 + (z - 8)), 1 + (1 + 1 + x11) + xs2), xs) :|: xs >= 0, xs2 >= 0, z' = 1 + (1 + 1 + (1 + (1 + 1 + x11) + xs2)) + xs, z - 8 >= 0, x11 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(7, z - 23), y3)), 1 + 7 + (1 + 10 + (z - 23))), 1 + 10 + y3), xs) :|: xs >= 0, z' = 1 + (1 + 1 + (1 + 10 + y3)) + xs, y3 >= 0, z - 23 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(3, f7), x)), 1 + (1 + (1 + 4 + 2) + f7) + x10), x), xs) :|: xs >= 0, x >= 0, f7 >= 0, x10 >= 0, z = 1 + 3 + (1 + (1 + (1 + 4 + 2) + f7) + x10), z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(1, x9), app(app(3, f6), x))), 1 + (1 + (1 + 4 + 11) + f6) + x9), x), xs) :|: xs >= 0, z = 1 + 3 + (1 + (1 + (1 + 4 + 11) + f6) + x9), x >= 0, f6 >= 0, x9 >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(app(1, app(z - 11, x8)), app(app(6, z - 11), xs1))), 1 + 6 + (z - 11)), 1 + (1 + 1 + x8) + xs1), xs) :|: xs >= 0, x8 >= 0, xs1 >= 0, z - 11 >= 0, z' = 1 + (1 + 1 + (1 + (1 + 1 + x8) + xs1)) + xs
   app(z, z') -{ 2 }-> app(app(app(app(4, app(10, app(app(9, app(app(7, z - 25), y4)), app(10, y4)))), 1 + 9 + (1 + 10 + (z - 25))), 1 + 10 + y4), xs) :|: xs >= 0, y4 >= 0, z' = 1 + (1 + 1 + (1 + 10 + y4)) + xs, z - 25 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, app(10, app(5, app(10, app(app(9, x13), app(10, app(10, 0))))))), 5), 1 + 10 + (1 + 10 + x13)), xs) :|: z' = 1 + (1 + 1 + (1 + 10 + (1 + 10 + x13))) + xs, x13 >= 0, xs >= 0, z = 1 + 3 + 5
   app(z, z') -{ 2 }-> app(app(app(app(4, 8), 1 + 6 + (z - 11)), 8), z' - 11) :|: z - 11 >= 0, z' - 11 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, 8), 1 + 3 + (z - 8)), 8), z' - 11) :|: z' - 11 >= 0, z - 8 >= 0
   app(z, z') -{ 2 }-> app(app(app(app(4, 0), 5), 1 + 10 + 0), z' - 14) :|: z' - 14 >= 0, z = 1 + 3 + 5
   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 + y2), xs) :|: xs >= 0, z' = 1 + (1 + 1 + (1 + 10 + y2)) + xs, y2 >= 0, z = 1 + 3 + (1 + 9 + 0)
   app(z, z') -{ 2 }-> app(app(app(app(4, z - 12), 1 + 7 + (z - 12)), 0), z' - 3) :|: z' - 3 >= 0, z - 12 >= 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(1, app(z - 7, x)), app(app(6, z - 7), xs)) :|: z - 7 >= 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 + 7 + (z - 21), z' - 11)), 0)) :|: z - 21 >= 0, z' - 11 >= 0
   app(z, z') -{ 1 }-> app(10, app(app(9, app(1 + 7 + (z - 21), z' - 11)), 1 + 10 + (z' - 11))) :|: z - 21 >= 0, z' - 11 >= 0
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(0, app(10, 0))))) :|: z' - 22 >= 0, z = 5
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(0, app(10, 1 + 10 + 0))))) :|: z' - 22 >= 0, z = 5
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(1 + 9 + (z' - 22), app(10, 0))))) :|: z' - 22 >= 0, z = 5
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(1 + 9 + (z' - 22), app(10, 1 + 10 + 0))))) :|: z' - 22 >= 0, z = 5
   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 - 19 >= 0, z' - 11 >= 0
   app(z, z') -{ 1 }-> app(1 + 7 + (z - 19), z' - 11) :|: z - 19 >= 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 }-> 8 :|: z - 7 >= 0, z' = 8
   app(z, z') -{ 1 }-> 8 :|: z - 4 >= 0, z' = 8
   app(z, z') -{ 1 }-> 0 :|: z' = 1 + 10 + 0, z = 5
   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 - 8 :|: z - 8 >= 0, z' = 0
   app(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 9 :|: z = 9
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 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_log -{ 0 }-> 5 :|: 
   encode_log -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 6 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 7 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 8 :|: 
   encode_nil -{ 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 :|: 


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

(31) 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_log -> null_encode_log [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_log, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app

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

(32)
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(log, c_app(s, 0)) -> 0 [1]
   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(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(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(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, x), 0) -> x [1]
   app(log, c_app(s, c_app(s, x))) -> app(s, app(log, app(s, app(app(quot, x), app(s, app(s, 0)))))) [1]
   app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [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]
   encArg(minus) -> minus [0]
   encArg(0) -> 0 [0]
   encArg(s) -> s [0]
   encArg(quot) -> quot [0]
   encArg(log) -> log [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_log -> log [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_log -> null_encode_log [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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
s :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
0 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
map :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
cons :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
quot :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter2 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
true :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
filter :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
false :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
nil :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
minus :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encArg :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app
encode_log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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_log :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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 :: log:s:0:c_app:map:cons:quot:filter2:true:filter:false:nil:minus:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_quot:null_encode_log: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
----------------------------------------

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

   log => 5
   s => 10
   0 => 0
   map => 6
   cons => 1
   quot => 9
   filter2 => 4
   true => 11
   filter => 3
   false => 2
   nil => 8
   minus => 7
   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_log => 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

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

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

   app(z, z') -{ 1 }-> x :|: x >= 0, z = 1 + 7 + x, z' = 0
   app(z, z') -{ 1 }-> app(app(app(app(4, app(f, x)), f), x), xs) :|: z = 1 + 3 + f, f >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(app(7, x), y) :|: x >= 0, y >= 0, z = 1 + 7 + (1 + 10 + x), 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(6, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 6 + f, z' = 1 + (1 + 1 + x) + xs
   app(z, z') -{ 1 }-> app(10, app(app(9, app(app(7, x), y)), app(10, y))) :|: z = 1 + 9 + (1 + 10 + x), x >= 0, y >= 0, z' = 1 + 10 + y
   app(z, z') -{ 1 }-> app(10, app(5, app(10, app(app(9, x), app(10, app(10, 0)))))) :|: x >= 0, z' = 1 + 10 + (1 + 10 + x), z = 5
   app(z, z') -{ 1 }-> 8 :|: f >= 0, z = 1 + 6 + f, z' = 8
   app(z, z') -{ 1 }-> 8 :|: z = 1 + 3 + f, f >= 0, z' = 8
   app(z, z') -{ 1 }-> 0 :|: z' = 1 + 10 + 0, z = 5
   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 = v0, z' = v1
   app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1
   encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 9 :|: z = 9
   encArg(z) -{ 0 }-> 8 :|: z = 8
   encArg(z) -{ 0 }-> 7 :|: z = 7
   encArg(z) -{ 0 }-> 6 :|: z = 6
   encArg(z) -{ 0 }-> 5 :|: z = 5
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 11 :|: z = 11
   encArg(z) -{ 0 }-> 10 :|: z = 10
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_0 -{ 0 }-> 0 :|: 
   encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cons -{ 0 }-> 1 :|: 
   encode_cons -{ 0 }-> 0 :|: 
   encode_false -{ 0 }-> 2 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_filter -{ 0 }-> 3 :|: 
   encode_filter -{ 0 }-> 0 :|: 
   encode_filter2 -{ 0 }-> 4 :|: 
   encode_filter2 -{ 0 }-> 0 :|: 
   encode_log -{ 0 }-> 5 :|: 
   encode_log -{ 0 }-> 0 :|: 
   encode_map -{ 0 }-> 6 :|: 
   encode_map -{ 0 }-> 0 :|: 
   encode_minus -{ 0 }-> 7 :|: 
   encode_minus -{ 0 }-> 0 :|: 
   encode_nil -{ 0 }-> 8 :|: 
   encode_nil -{ 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.

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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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_log -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log) -> 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_LOG -> 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(log, app(s, 0)) -> c30
   APP(log, app(s, app(s, z0))) -> c31(APP(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0)))))), APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(s, app(app(quot, z0), app(s, app(s, 0)))), APP(app(quot, z0), app(s, app(s, 0))), APP(quot, z0), APP(s, app(s, 0)), APP(s, 0))
   APP(app(map, z0), nil) -> c32
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(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) -> c34
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(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) -> c36(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) -> c37(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(log, app(s, 0)) -> c30
   APP(log, app(s, app(s, z0))) -> c31(APP(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0)))))), APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(s, app(app(quot, z0), app(s, app(s, 0)))), APP(app(quot, z0), app(s, app(s, 0))), APP(quot, z0), APP(s, app(s, 0)), APP(s, 0))
   APP(app(map, z0), nil) -> c32
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(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) -> c34
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(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) -> c36(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) -> c37(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_log, 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_LOG, 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_7, c32, c33_5, c34, c35_5, c36_4, c37_2


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

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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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_log -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(log, app(s, app(s, z0))) -> c31(APP(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0)))))), APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(s, app(app(quot, z0), app(s, app(s, 0)))), APP(app(quot, z0), app(s, app(s, 0))), APP(quot, z0), APP(s, app(s, 0)), APP(s, 0))
   APP(app(map, z0), nil) -> c32
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(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) -> c34
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(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) -> c36(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) -> c37(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(log, app(s, 0)) -> c30
   APP(log, app(s, app(s, z0))) -> c31(APP(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0)))))), APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(s, app(app(quot, z0), app(s, app(s, 0)))), APP(app(quot, z0), app(s, app(s, 0))), APP(quot, z0), APP(s, app(s, 0)), APP(s, 0))
   APP(app(map, z0), nil) -> c32
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(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) -> c34
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(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) -> c36(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) -> c37(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_log, 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_7, c32, c33_5, c34, c35_5, c36_4, c37_2


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

(39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 20 trailing tuple parts
----------------------------------------

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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_log -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(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_log, 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, c32, c34, c27_1, c29_2, c31_2, c33_2, c35_2, c36_1, c37_1


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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_log -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   ENCODE_APP(z0, z1) -> c(ENCARG(z0))
   ENCODE_APP(z0, z1) -> c(ENCARG(z1))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(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_log, 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, c32, c34, c27_1, c29_2, c31_2, c33_2, c35_2, c36_1, c37_1, c_1


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

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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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_log -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(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_log, 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, c32, c34, c27_1, c29_2, c31_2, c33_2, c35_2, c36_1, c37_1, c_1


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

(45) 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_log -> log
   encode_map -> map
   encode_nil -> nil
   encode_cons -> cons
   encode_filter -> filter
   encode_filter2 -> filter2
   encode_true -> true
   encode_false -> false

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   ENCARG_1, APP_2, ENCODE_APP_2

Compound Symbols:   c12_3, c26, c28, c30, c32, c34, c27_1, c29_2, c31_2, c33_2, c35_2, c36_1, c37_1, c_1


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

(47) 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, log)) -> c12(APP(encArg(x0), log), ENCARG(x0), ENCARG(log))
   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(log, x1)) -> c12(APP(log, encArg(x1)), ENCARG(log), 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))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   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, log)) -> c12(APP(encArg(x0), log), ENCARG(x0), ENCARG(log))
   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(log, x1)) -> c12(APP(log, encArg(x1)), ENCARG(log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c26, c28, c30, c32, c34, c27_1, c29_2, c31_2, c33_2, c35_2, c36_1, c37_1, c_1, c12_3


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

(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 35 trailing tuple parts
----------------------------------------

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   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(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
K tuples:none
Defined Rule Symbols:   encArg_1, app_2

Defined Pair Symbols:   APP_2, ENCODE_APP_2, ENCARG_1

Compound Symbols:   c26, c28, c30, c32, c34, c27_1, c29_2, c31_2, c33_2, c35_2, c36_1, c37_1, c_1, c12_3, c12_2, c12_1


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

(51) 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)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0))))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, c32, c34, c27_1, c31_2, c33_2, c35_2, c36_1, c37_1, c_1, c12_3, c12_2, c12_1, c29_2


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(log, app(s, app(s, z0))) -> c31(APP(log, app(s, app(app(quot, z0), app(s, app(s, 0))))), APP(app(quot, z0), app(s, app(s, 0)))) by 
   APP(log, app(s, app(s, 0))) -> c31(APP(log, app(s, 0)), APP(app(quot, 0), app(s, app(s, 0))))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, 0))) -> c31(APP(log, app(s, 0)), APP(app(quot, 0), app(s, app(s, 0))))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, 0))) -> c31(APP(log, app(s, 0)), APP(app(quot, 0), app(s, app(s, 0))))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, 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, c32, c34, c27_1, c33_2, c35_2, c36_1, c37_1, c_1, c12_3, c12_2, c12_1, c29_2, c31_2, c31_1


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

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, 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, c32, c34, c27_1, c33_2, c35_2, c36_1, c37_1, c_1, c12_3, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(app(app(app(filter2, 0), log), app(s, 0)), x2), APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(app(app(app(filter2, app(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0))))))), log), app(s, app(s, z0))), x2), APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(app(app(app(filter2, 0), log), app(s, 0)), x2), APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(app(app(app(filter2, app(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0))))))), log), app(s, app(s, z0))), x2), APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(app(app(app(filter2, 0), log), app(s, 0)), x2), APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(app(app(app(filter2, app(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0))))))), log), app(s, app(s, z0))), x2), APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c_1, c12_3, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2


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

(59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing tuple parts
----------------------------------------

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1)))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c_1, c12_3, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by 
   ENCODE_APP(x0, 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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, 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)))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_3, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1


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

(63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 11 trailing nodes:
   ENCODE_APP(true, x1) -> c(APP(true, encArg(x1)))
   ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1)))
   ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1)))
   ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1)))
   ENCODE_APP(false, x1) -> c(APP(false, encArg(x1)))
   ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1)))
   ENCODE_APP(map, x1) -> c(APP(map, encArg(x1)))
   ENCODE_APP(quot, x1) -> c(APP(quot, encArg(x1)))
   ENCODE_APP(0, x1) -> c(APP(0, encArg(x1)))
   ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1)))
   ENCODE_APP(s, x1) -> c(APP(s, encArg(x1)))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_3, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1


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

(65) 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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), ENCARG(log), 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)))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), ENCARG(log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_3, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1


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

(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 23 trailing tuple parts
----------------------------------------

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_3, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1


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

(69) 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), ENCARG(cons_app(x0, x1)), ENCARG(log))
   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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), ENCARG(cons_app(x0, x1)), ENCARG(log))
   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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(73) 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(log, minus)) -> c12(APP(log, minus), ENCARG(log))
   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)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, minus)) -> c12(APP(log, minus), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(75) 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(log, minus)) -> c12(APP(log, minus), ENCARG(log))
   ENCARG(cons_app(minus, minus)) -> c12(APP(minus, minus), ENCARG(minus))
   ENCARG(cons_app(0, minus)) -> c12(APP(0, minus), ENCARG(0))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(77) 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(log, 0)) -> c12(APP(log, 0), ENCARG(log))
   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)))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, 0)) -> c12(APP(log, 0), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(nil, 0)) -> c12(APP(nil, 0), ENCARG(nil))
   ENCARG(cons_app(true, 0)) -> c12(APP(true, 0), ENCARG(true))
   ENCARG(cons_app(s, 0)) -> c12(APP(s, 0), ENCARG(s))
   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(cons, 0)) -> c12(APP(cons, 0), ENCARG(cons))
   ENCARG(cons_app(log, 0)) -> c12(APP(log, 0), ENCARG(log))
   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(0, 0)) -> c12(APP(0, 0), ENCARG(0))
   ENCARG(cons_app(map, 0)) -> c12(APP(map, 0), ENCARG(map))
   ENCARG(cons_app(minus, 0)) -> c12(APP(minus, 0), ENCARG(minus))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(81) 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(log, s)) -> c12(APP(log, s), ENCARG(log))
   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)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, s)) -> c12(APP(log, s), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, quot)) -> c12(APP(encArg(x0), quot), ENCARG(x0))
   ENCARG(cons_app(x0, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(85) 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(log, quot)) -> c12(APP(log, quot), ENCARG(log))
   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)))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, quot)) -> c12(APP(log, quot), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   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(true, quot)) -> c12(APP(true, quot), ENCARG(true))
   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(log, quot)) -> c12(APP(log, quot), ENCARG(log))
   ENCARG(cons_app(filter, quot)) -> c12(APP(filter, quot), ENCARG(filter))
   ENCARG(cons_app(map, quot)) -> c12(APP(map, quot), ENCARG(map))
   ENCARG(cons_app(filter2, quot)) -> c12(APP(filter2, quot), ENCARG(filter2))
   ENCARG(cons_app(s, quot)) -> c12(APP(s, quot), ENCARG(s))
   ENCARG(cons_app(false, quot)) -> c12(APP(false, quot), ENCARG(false))
   ENCARG(cons_app(nil, quot)) -> c12(APP(nil, quot), ENCARG(nil))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   ENCARG(cons_app(x0, log)) -> c12(APP(encArg(x0), log), 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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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, log)) -> c12(APP(minus, log), ENCARG(minus))
   ENCARG(cons_app(0, log)) -> c12(APP(0, log), ENCARG(0))
   ENCARG(cons_app(s, log)) -> c12(APP(s, log), ENCARG(s))
   ENCARG(cons_app(quot, log)) -> c12(APP(quot, log), ENCARG(quot))
   ENCARG(cons_app(log, log)) -> c12(APP(log, log), ENCARG(log))
   ENCARG(cons_app(map, log)) -> c12(APP(map, log), ENCARG(map))
   ENCARG(cons_app(nil, log)) -> c12(APP(nil, log), ENCARG(nil))
   ENCARG(cons_app(cons, log)) -> c12(APP(cons, log), ENCARG(cons))
   ENCARG(cons_app(filter, log)) -> c12(APP(filter, log), ENCARG(filter))
   ENCARG(cons_app(filter2, log)) -> c12(APP(filter2, log), ENCARG(filter2))
   ENCARG(cons_app(true, log)) -> c12(APP(true, log), ENCARG(true))
   ENCARG(cons_app(false, log)) -> c12(APP(false, log), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(93) 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(log, map)) -> c12(APP(log, map), ENCARG(log))
   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)))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, map)) -> c12(APP(log, map), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(97) 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(log, nil)) -> c12(APP(log, nil), ENCARG(log))
   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)))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, nil)) -> c12(APP(log, nil), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(101) 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(log, cons)) -> c12(APP(log, cons), ENCARG(log))
   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)))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, cons)) -> c12(APP(log, cons), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(105) 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(log, filter)) -> c12(APP(log, filter), ENCARG(log))
   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)))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, filter)) -> c12(APP(log, filter), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(109) 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(log, filter2)) -> c12(APP(log, filter2), ENCARG(log))
   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)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, filter2)) -> c12(APP(log, filter2), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   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(s, filter2)) -> c12(APP(s, filter2), ENCARG(s))
   ENCARG(cons_app(0, filter2)) -> c12(APP(0, filter2), ENCARG(0))
   ENCARG(cons_app(log, filter2)) -> c12(APP(log, filter2), ENCARG(log))
   ENCARG(cons_app(false, filter2)) -> c12(APP(false, filter2), ENCARG(false))
   ENCARG(cons_app(filter2, filter2)) -> c12(APP(filter2, filter2), ENCARG(filter2))
   ENCARG(cons_app(nil, filter2)) -> c12(APP(nil, filter2), ENCARG(nil))
   ENCARG(cons_app(true, filter2)) -> c12(APP(true, filter2), ENCARG(true))
   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(minus, filter2)) -> c12(APP(minus, filter2), ENCARG(minus))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(113) 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(log, true)) -> c12(APP(log, true), ENCARG(log))
   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)))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, true)) -> c12(APP(log, true), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_2, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(117) 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(log, false)) -> c12(APP(log, false), ENCARG(log))
   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)))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, false)) -> c12(APP(log, false), ENCARG(log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c12_2, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

(119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCARG(cons_app(s, false)) -> c12(APP(s, false), ENCARG(s))
   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(map, false)) -> c12(APP(map, false), ENCARG(map))
   ENCARG(cons_app(log, false)) -> c12(APP(log, false), ENCARG(log))
   ENCARG(cons_app(true, false)) -> c12(APP(true, false), ENCARG(true))
   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(false, false)) -> c12(APP(false, false), ENCARG(false))
   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(filter2, false)) -> c12(APP(filter2, false), ENCARG(filter2))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, x1)) -> c12(APP(log, encArg(x1)), 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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c12_2, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3


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

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

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, minus)) -> c12(APP(log, minus), ENCARG(minus))
   ENCARG(cons_app(log, 0)) -> c12(APP(log, 0), ENCARG(0))
   ENCARG(cons_app(log, s)) -> c12(APP(log, s), ENCARG(s))
   ENCARG(cons_app(log, quot)) -> c12(APP(log, quot), ENCARG(quot))
   ENCARG(cons_app(log, log)) -> c12(APP(log, log), ENCARG(log))
   ENCARG(cons_app(log, map)) -> c12(APP(log, map), ENCARG(map))
   ENCARG(cons_app(log, nil)) -> c12(APP(log, nil), ENCARG(nil))
   ENCARG(cons_app(log, cons)) -> c12(APP(log, cons), ENCARG(cons))
   ENCARG(cons_app(log, filter)) -> c12(APP(log, filter), ENCARG(filter))
   ENCARG(cons_app(log, filter2)) -> c12(APP(log, filter2), ENCARG(filter2))
   ENCARG(cons_app(log, true)) -> c12(APP(log, true), ENCARG(true))
   ENCARG(cons_app(log, false)) -> c12(APP(log, false), ENCARG(false))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2


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

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

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2


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

(125) 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)))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(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)) -> c35(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(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(minus, app(s, x0)), app(s, x1)))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 0), log), app(s, 0)), x2)), app(filter, log)), app(app(cons, app(s, 0)), x2)), x3), APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0))))))), log), app(s, app(s, z0))), x2)), app(filter, log)), app(app(cons, app(s, app(s, z0))), x2)), x3), APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 0), log), app(s, 0)), x2)), app(filter, log)), app(app(cons, app(s, 0)), x2)), x3), APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0))))))), log), app(s, app(s, z0))), x2)), app(filter, log)), app(app(cons, app(s, app(s, z0))), x2)), x3), APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 0), log), app(s, 0)), x2)), app(filter, log)), app(app(cons, app(s, 0)), x2)), x3), APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(s, app(log, app(s, app(app(quot, z0), app(s, app(s, 0))))))), log), app(s, app(s, z0))), x2)), app(filter, log)), app(app(cons, app(s, app(s, z0))), x2)), x3), APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing tuple parts
----------------------------------------

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(137) 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(log, minus) -> c(APP(log, 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))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, minus) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

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

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(141) 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(log, 0) -> c(APP(log, 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))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, 0) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

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

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(145) 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(log, s) -> c(APP(log, 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))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, s) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   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(0, s) -> c(APP(0, s))
   ENCODE_APP(false, s) -> c(APP(false, s))
   ENCODE_APP(log, s) -> c(APP(log, s))
   ENCODE_APP(filter, s) -> c(APP(filter, s))
   ENCODE_APP(filter2, s) -> c(APP(filter2, s))
   ENCODE_APP(nil, s) -> c(APP(nil, s))
   ENCODE_APP(s, s) -> c(APP(s, s))
   ENCODE_APP(true, s) -> c(APP(true, s))
   ENCODE_APP(map, s) -> c(APP(map, s))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, quot) -> c(APP(encArg(x0), quot))
   ENCODE_APP(x0, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(149) 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(log, quot) -> c(APP(log, 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))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, quot) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

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

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2))
   ENCODE_APP(x0, log) -> c(APP(encArg(x0), log))
   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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

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

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, log) -> c(APP(minus, log))
   ENCODE_APP(0, log) -> c(APP(0, log))
   ENCODE_APP(s, log) -> c(APP(s, log))
   ENCODE_APP(quot, log) -> c(APP(quot, log))
   ENCODE_APP(log, log) -> c(APP(log, log))
   ENCODE_APP(map, log) -> c(APP(map, log))
   ENCODE_APP(nil, log) -> c(APP(nil, log))
   ENCODE_APP(cons, log) -> c(APP(cons, log))
   ENCODE_APP(filter, log) -> c(APP(filter, log))
   ENCODE_APP(filter2, log) -> c(APP(filter2, log))
   ENCODE_APP(true, log) -> c(APP(true, log))
   ENCODE_APP(false, log) -> c(APP(false, log))
   ENCODE_APP(cons_app(z0, z1), log) -> c(APP(app(encArg(z0), encArg(z1)), log))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

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

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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), log) -> c(APP(app(encArg(z0), encArg(z1)), log))
S tuples:
   APP(app(minus, z0), 0) -> c26
   APP(app(quot, 0), app(s, z0)) -> c28
   APP(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(157) 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(log, map) -> c(APP(log, 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))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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), log) -> c(APP(app(encArg(z0), encArg(z1)), log))
   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(log, map) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(159) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   ENCODE_APP(log, map) -> c(APP(log, map))
   ENCODE_APP(map, map) -> c(APP(map, map))
   ENCODE_APP(s, map) -> c(APP(s, 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(filter, map) -> c(APP(filter, 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(minus, map) -> c(APP(minus, map))
   ENCODE_APP(nil, map) -> c(APP(nil, map))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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), log) -> c(APP(app(encArg(z0), encArg(z1)), log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(161) 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(log, nil) -> c(APP(log, 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))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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), log) -> c(APP(app(encArg(z0), encArg(z1)), log))
   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(log, nil) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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), log) -> c(APP(app(encArg(z0), encArg(z1)), log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

(165) 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(log, cons) -> c(APP(log, 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))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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), log) -> c(APP(app(encArg(z0), encArg(z1)), log))
   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(log, cons) -> c(APP(log, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1


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

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

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(minus) -> minus
   encArg(0) -> 0
   encArg(s) -> s
   encArg(quot) -> quot
   encArg(log) -> log
   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(log, app(s, 0)) -> 0
   app(log, app(s, app(s, z0))) -> app(s, app(log, app(s, app(app(quot, z0), app(s, 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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   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(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(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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(log, x1) -> c(APP(log, encArg(x1)))
   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, log))) -> c12(APP(encArg(x0), app(encArg(x1), log)), ENCARG(x0), ENCARG(cons_app(x1, log)))
   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(log, x2))) -> c12(APP(encArg(x0), app(log, encArg(x2))), ENCARG(x0), ENCARG(cons_app(log, 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(log, cons_app(x1, x2))) -> c12(APP(log, app(encArg(x1), encArg(x2))), 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, log), x2)) -> c12(APP(app(encArg(x0), log), encArg(x2)), ENCARG(cons_app(x0, log)), 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(log, x1), x2)) -> c12(APP(app(log, encArg(x1)), encArg(x2)), ENCARG(cons_app(log, 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), log)) -> c12(APP(app(encArg(x0), encArg(x1)), log), 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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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), log) -> c(APP(app(encArg(z0), encArg(z1)), log))
   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(log, app(s, 0)) -> c30
   APP(app(map, z0), nil) -> c32
   APP(app(filter, z0), nil) -> c34
   APP(app(minus, app(s, z0)), app(s, z1)) -> c27(APP(app(minus, z0), z1))
   APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2))
   APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2))
   APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2))
   APP(app(quot, app(s, z0)), app(s, 0)) -> c29(APP(app(quot, z0), app(s, 0)), APP(app(minus, z0), 0))
   APP(log, app(s, app(s, app(s, z0)))) -> c31(APP(log, app(s, app(s, app(app(quot, app(app(minus, z0), app(s, 0))), app(s, app(s, 0)))))), APP(app(quot, app(s, z0)), app(s, app(s, 0))))
   APP(log, app(s, app(s, x0))) -> c31(APP(app(quot, x0), app(s, app(s, 0))))
   APP(log, app(s, app(s, 0))) -> c1(APP(log, app(s, 0)))
   APP(log, app(s, app(s, 0))) -> c1(APP(app(quot, 0), app(s, app(s, 0))))
   APP(app(filter, app(minus, z0)), app(app(cons, 0), x2)) -> c35(APP(app(app(app(filter2, z0), app(minus, z0)), 0), x2), APP(app(minus, z0), 0))
   APP(app(filter, app(quot, 0)), app(app(cons, app(s, z0)), x2)) -> c35(APP(app(quot, 0), app(s, z0)))
   APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c35(APP(app(quot, app(s, z0)), app(s, z1)))
   APP(app(filter, log), app(app(cons, app(s, 0)), x2)) -> c35(APP(log, app(s, 0)))
   APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)) -> c35(APP(log, app(s, app(s, z0))))
   APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil))
   APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2)))
   APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil))
   APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(filter, app(quot, app(s, z0))), app(app(cons, app(s, z1)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, 0)), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, 0)), x2)))
   APP(app(filter, app(filter, log)), app(app(cons, app(app(cons, app(s, app(s, z0))), x2)), x3)) -> c35(APP(app(filter, log), app(app(cons, app(s, app(s, z0))), x2)))
   APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(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)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2))
   APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(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, c32, c34, c27_1, c33_2, c36_1, c37_1, c12_1, c29_2, c31_2, c31_1, c1_1, c35_2, c35_1, c_1, c12_3, c12_2, c29_1